Exhibit 10.38

COBALT INTERNATIONAL ENERGY, INC.

LONG TERM INCENTIVE PLAN

Stock Appreciation Right Award Agreement

[Year] Grant

You have been granted a stock appreciation right (the “SAR”) that represents a right to acquire shares of Cobalt International Energy, Inc. (this “Award”) on the following terms and subject to the provisions of Attachment A and the Cobalt International Energy, Inc. Long Term Incentive Plan (the “Plan”).  Unless defined in this Award Agreement (including Attachment A, this “Agreement”), capitalized terms will have the meanings assigned to them in the Plan.  In the event of a conflict among the provisions of the Plan, this Agreement and any descriptive materials provided to you, the provisions of the Plan will prevail.

Attachment A

Stock Appreciation Right Award Agreement

Terms and Conditions

Grant to:  [Name]

Section 1.  Grant of Award.  Subject to the terms and conditions of the Plan and this Agreement, the Company hereby grants the SAR to the Participant on the Grant Date on the terms set forth on the cover page of this Agreement, as more fully described in this Attachment A.  The SAR represents the right to acquire up to, but not exceeding in the aggregate, the number of Shares set forth on the cover page of this Agreement.  This Award is granted under the Plan, which is incorporated herein by reference and made a part of this Agreement.

Section 2.  Vesting of Award.

(a)                       Termination of Service.

(i)                                     Death or Disability.  In the event of the Participant’s Termination of Service at any time due to the Participant’s death or Disability, any unvested portion of the SAR shall fully vest as of the date of such termination and the SAR shall remain exercisable until the Expiration Date.

(ii)                                  Termination for Cause.  In the event of the Participant’s Termination of Service by the Company for Cause, any unvested portion of the SAR and any vested portion of the SAR not yet exercised shall be forfeited in its entirety as of the date of such termination without any payment to the Participant.

(iii)                               Resignation by the Participant.  In the event of the Participant’s Termination of Service at any time by the Participant for any reason, any unvested portion of the SAR shall be forfeited in its entirety as of the date of such termination without any payment to the Participant and any vested portion of the SAR shall remain exercisable until the Expiration Date.

(iv)                              Termination without Cause.  In the event of the Participant’s Termination of Service at any time by the Company without Cause, any unvested portion of the SAR shall be forfeited in its entirety as of the date of such termination without any payment to the Participant and any vested portion of the SAR shall remain exercisable until the earlier of (i) 90 days following such Termination of Service and (ii) the Expiration Date.

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(b)                                 Change in Control.  If a Change in Control occurs at any time, the SAR shall be canceled in consideration of the full acceleration value of the SAR and, at the Participant’s election pursuant to such procedures as the Committee determines, (i) a cash payment in an amount equal to the Intrinsic Value of the SAR (which may be equal to but not less than zero), which, if in excess of zero, shall be payable upon the effective date of such Change in Control, or (ii) a stock appreciation right to acquire shares of the common stock of, as applicable, the acquirer, the surviving entity or the ultimate parent thereof (the Intrinsic Value of which stock appreciation right as of immediately following such Change in Control shall equal the Intrinsic Value of the SAR immediately prior to such Change in Control).  Notwithstanding the Participant’s election pursuant to the preceding sentence, the Company’s Chief Executive Officer may determine that all or a portion of the SAR shall be treated in accordance with either of clauses (i) or (ii) of the preceding sentence; provided that such treatment is substantially similar to the treatment applicable to the stock appreciation rights to acquire Shares then held by other participants generally.

Section 3.  Exercise of SAR.

(a)                                 Right to Exercise.  The SAR shall be exercisable on or prior to the Expiration Date in accordance with the vesting schedule and applicable provisions set forth in this Agreement and the Plan.

(b)                                 Method of Exercise.

(i)                           The vested portion of the SAR shall be exercisable by delivery of an exercise notice in the form attached as Exhibit A (the “Exercise Notice”) which shall state the election to exercise the SAR, the number of Shares with respect to which the SAR is being exercised, and such other representations and agreements as may be required by the Company; provided that the SAR may be exercised with respect to whole Shares only.  The SAR shall be deemed to be exercised upon receipt by the Company of such fully executed Exercise Notice and the satisfaction of any tax withholding requirements.

(ii)                        Upon exercise of the SAR, the Company shall deliver to the Participant, at the Company’s discretion, (i) Shares issued in the Participant’s name for the number of Shares, to the nearest number of whole Shares, (ii) cash or (iii) a combination of Shares and cash, which represent the excess (if any) of the Fair Market Value of the Shares underlying the portion of the SAR that is being exercised on the date of exercise over the aggregate exercise price of such Shares.

(iii)                     No Shares shall be issued pursuant to the exercise of an SAR unless such issuance and such exercise comply with all applicable laws and regulations.  Assuming such compliance, for income tax

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purposes the Shares shall be considered transferred to the Participant on the date on which the SAR is exercised with respect to such Shares.

(c)                                  Transferability.  The SAR may not be assigned, sold, transferred or otherwise be subject to alienation by the Participant other than by will; provided, that, the designation of a beneficiary shall not constitute an assignment, sale, transfer or alienation.

(d)                                 Withholding.  No Shares or cash will be issued pursuant to the exercise of this SAR unless and until the Participant shall have remitted to the Company an amount sufficient to satisfy any federal, state or local withholding tax requirements, or shall have made other arrangements satisfactory to the Company with respect to such taxes.  The Participant may elect that all or any part of such withholding requirement be satisfied by retention by the Company of a portion of the Shares and/or cash acquired upon exercise of the SAR.  If such election is made, the Shares and/or cash so retained shall be credited against such withholding requirement at the fair market value of the Shares on the date of exercise.

Section 4.  Miscellaneous Provisions.

(a)                                 Notices.  All notices, requests and other communications under this Agreement shall be in writing and shall be delivered in person (by courier or otherwise), mailed by certified or registered mail, return receipt requested, or sent by facsimile transmission, as follows:

if to the Company, to:

Cobalt International Energy, Inc.

Cobalt Center

920 Memorial City Way, Suite 100

Houston, TX 77024

Attention: General Counsel

Facsimile: 713-579-9184

if to the Participant, to the address that the Participant most recently provided to the Company,

or to such other address or facsimile number as such party may hereafter specify for the purpose by notice to the other parties hereto.  All such notices, requests and other communications shall be deemed received on the date of receipt by the recipient thereof if received prior to 5:00 p.m. on a business day in the place of receipt.  Otherwise, any such notice, request or communication shall be deemed received on the next succeeding business day in the place of receipt.

(b)                                 Entire Agreement.  This Agreement, the Plan, and any other agreements referred to herein and therein and any schedules, exhibits and other documents referred to herein or therein, constitute the entire agreement and

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understanding between the parties in respect of the subject matter hereof and supersede all prior and contemporaneous arrangements, agreements and understandings, both oral and written, whether in term sheets, presentations or otherwise, between the parties with respect to the subject matter hereof.

(c)                                  Amendment; Waiver.  No amendment or modification of any provision of this Agreement shall be effective unless signed in writing by or on behalf of the Company and the Participant, except that the Company may amend or modify this Agreement without the Participant’s consent in accordance with the provisions of the Plan or as otherwise set forth in this Agreement.  No waiver of any breach or condition of this Agreement shall be deemed to be a waiver of any other or subsequent breach or condition whether of like or different nature.  Any amendment or modification of or to any provision of this Agreement, or any waiver of any provision of this Agreement, shall be effective only in the specific instance and for the specific purpose for which made or given.

(d)                                 Assignment.  Neither this Agreement nor any right, remedy, obligation or liability arising hereunder or by reason hereof shall be assignable by the Participant.

(e)                                  Successors and Assigns; No Third Party Beneficiaries.  This Agreement shall inure to the benefit of and be binding upon the Company and the Participant and their respective heirs, successors, legal representatives and permitted assigns.  Nothing in this Agreement, expressed or implied, is intended to confer on any person other than the Company and the Participant, and their respective heirs, successors, legal representatives and permitted assigns, any rights, remedies, obligations or liabilities under or by reason of this Agreement.

(f)                                   Counterparts.  This Agreement may be signed in any number of counterparts, each of which shall be an original, with the same effect as if the signatures thereto and hereto were upon the same instrument.

(g)                                  Participant Undertaking.  The Participant agrees to take whatever additional action and execute whatever additional documents the Company may deem necessary or advisable to carry out or give effect to any of the obligations or restrictions imposed on either the Participant or this Award pursuant to the provisions of this Agreement.

(h)                                 Plan.  The Participant acknowledges and understands that material definitions and provisions concerning this Award and the Participant’s rights and obligations with respect thereto are set forth in the Plan.  The Participant has read carefully, and understands, the provisions of the Plan.

(i)                                     Governing Law.  The Agreement shall be governed by the laws of the State of Delaware, without application of the conflicts of law principles thereof.

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(j)                                    No Right to Continued Service.  The granting of the Award evidenced hereby and this Agreement shall impose no obligation on the Company or any Affiliate to continue the service of the Participant and shall not lessen or affect the right that the Company or any Affiliate may have to terminate the service of such Participant.

(k)                                 Jurisdiction.  The parties hereto agree that any suit, action or proceeding seeking to enforce any provision of, or based on any matter arising out of or in connection with, this Agreement or the transactions contemplated hereby (whether brought by any party or any of its affiliates or against any party or any of its affiliates) shall be brought in the Delaware Chancery Court or, if such court shall not have jurisdiction, any federal court located in the State of Delaware or other Delaware state court, and each of the parties hereby irrevocably consents to the jurisdiction of such courts (and of the appropriate appellate courts therefrom) in any such suit, action or proceeding and irrevocably waives, to the fullest extent permitted by law, any objection that it may now or hereafter have to the laying of the venue of any such suit, action or proceeding in any such court or that any such suit, action or proceeding brought in any such court has been brought in an inconvenient forum.  Process in any such suit, action or proceeding may be served on each party anywhere in the world, whether within or without the jurisdiction of any such court.  Without limiting the foregoing, each party agrees that service of process on such party as provided in Section 5(a) shall be deemed effective service of process on such party.

(l)                                     WAIVER OF JURY TRIAL.  EACH OF THE PARTIES HERETO IRREVOCABLY WAIVES ANY AND ALL RIGHT TO TRIAL BY JURY IN ANY LEGAL PROCEEDING ARISING OUT OF OR RELATED TO THIS AGREEMENT OR THE TRANSACTIONS CONTEMPLATED HEREBY.

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IN WITNESS WHEREOF, the parties have executed this Agreement as of the day and year first written above.

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EXHIBIT A

COBALT INTERNATIONAL ENERGY, INC.

LONG TERM INCENTIVE PLAN

STOCK APPRECIATION RIGHT EXERCISE NOTICE

Cobalt International Energy, Inc.

Cobalt Center

920 Memorial City Way, Suite 100

Houston, TX 77024

Attention: [Secretary]

1.                                      Exercise of Stock Appreciation Right.  Effective as of today,                             (date), the undersigned (“Participant”) hereby elects to exercise Participant’s stock appreciation right (the “SAR”) with respect to                                shares of the common stock (the “Shares”) of Cobalt International Energy, Inc. (the “Company”) under and pursuant to the Long Term Incentive Plan (the “Plan”) and the SAR Award Agreement dated                                        (the “Award Agreement”).  Unless otherwise defined herein, the terms defined in the Plan and Award Agreement shall have the same defined meanings in this Exercise Notice.

2.                                      Representations of Participant.  Participant acknowledges that Participant has received, read and understood the Award Agreement and the Plan, and agrees to abide by and be bound by their terms and conditions.

3.                                      Rights as Shareholder.  Until the issuance of the Shares (as evidenced by the appropriate entry on the books of the Company or of a duly authorized transfer agent of the Company or as otherwise determined by the Committee), no right to vote or receive dividends or any other rights as a shareholder shall exist with respect to the Shares that are subject to the SAR, notwithstanding the exercise of the SAR.  The Shares shall be issued to Participant as soon as practicable after the SAR is exercised.  No adjustment shall be made for a dividend or other right for which the record date is prior to the date of issuance.

4.                                      Tax Consultation.  Participant understands that Participant may have a tax liability as a result of Participant’s acquisition or disposition of the Shares underlying the SAR.  Participant represents that Participant has consulted with any tax consultants Participant deems advisable in connection with the purchase or disposition of the Shares and that Participant is not relying on the Company for any tax advice.

5.                                      Successors and Assigns. The Company may assign any of its rights under this Agreement to single or multiple assignees, and this Agreement shall inure to the benefit of the successors and assigns of the Company.  Subject to the

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restrictions on transfer herein set forth, this Exercise Notice shall be binding upon Participant and his or her heirs, executors, administrators, successors and assigns.

6.                                      Interpretation.  Any dispute regarding the interpretation of this Exercise Notice shall be submitted by Participant or by the Company forthwith to the Compensation Committee of the Board of Directors of the Company (the “Committee”).  The resolution of such a dispute by the Committee shall be final and binding on all parties.

7.                                      Governing Law.  This Exercise Notice is governed by the internal substantive laws but not the choice of law rules, of the State of Delaware.

8.                                      Entire Agreement.  The Plan and the Award Agreement are incorporated herein by reference, and together with this Exercise Notice constitute the entire agreement of the parties with respect to the subject matter hereof and supersede in their entirety all prior undertakings and agreements of the Company and Participant with respect to the subject matter hereof.

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