Exhibit 10.3

TARGACEPT, INC.

2006 STOCK INCENTIVE PLAN

Nonqualified Stock Option Agreement

(Nonemployee Directors)

THIS AGREEMENT (together with Schedule A, attached hereto, the “Agreement”), effective as of the date specified as the “Grant Date” on Schedule A attached hereto, between TARGACEPT, INC., a Delaware corporation (the “Corporation”), and the individual identified on Schedule A attached hereto, a Nonemployee Director of the Corporation or an Affiliate (the “Participant”);

R E C I T A L S :

In furtherance of the purposes of the Targacept, Inc. 2006 Stock Incentive Plan, as amended or restated and as it may be hereafter amended or restated (the “Plan”), the Corporation and the Participant hereby agree as follows:

1. Incorporation of Plan. The rights and duties of the Corporation and the Participant under this Agreement shall in all respects be subject to and governed by the provisions of the Plan, the terms of which are incorporated herein by reference. In the event of any conflict between the provisions in the Agreement and those of the Plan, the provisions of the Plan shall govern. Unless otherwise defined herein, capitalized terms in this Agreement shall have the same definitions as set forth in the Plan.

2. Grant of Option; Term of Option. The Corporation hereby grants to the Participant pursuant to the Plan, as a matter of separate inducement and agreement in connection with his or her service to the Corporation, and not in lieu of any salary or other compensation for his or her services, the right and option (the “Option”) to purchase all or any part of such aggregate number of shares (the “Shares”) of common stock of the Corporation (the “Common Stock”) at a purchase price (the “Option Price”) as specified on Schedule A, attached hereto, and subject to such other terms and conditions as may be stated herein or in the Plan or on Schedule A. The Participant expressly acknowledges that the terms of Schedule A shall be incorporated herein by reference and shall constitute part of this Agreement. The Corporation and the Participant further acknowledge and agree that the signatures of the Corporation and the Participant on the Grant Notice contained in Schedule A shall constitute their acceptance of all of the terms of this Agreement and their agreement to be bound by the terms of this Agreement. The Option shall be designated as a Nonqualified Option, as stated on Schedule A. Except as otherwise provided in the Plan or this Agreement, this Option will expire if not exercised in full by the Expiration Date specified on Schedule A.

3. Exercise of Option. Subject to the terms of the Plan and this Agreement, the Option shall become exercisable on the date or dates, and subject to such conditions, as are set forth on Schedule A attached hereto. To the extent that the Option is exercisable and not exercised, the Option shall accumulate and be exercisable by the Participant in whole or in part at any time

prior to expiration of the Option, subject to the terms of the Plan and this Agreement. The Participant expressly acknowledges that the Option may vest and be exercisable only upon such terms and conditions as are provided in this Agreement and the Plan. Upon the exercise of an Option in whole or in part and payment of the Option Price in accordance with the provisions of the Plan and this Agreement, the Corporation shall, as soon thereafter as practicable, deliver to the Participant a certificate or certificates for the Shares purchased. Payment of the Option Price may be made (i) in cash or by cash equivalent; and, where permitted by applicable law, payment may also be made (ii) by delivery (by either actual delivery or attestation) of shares of Common Stock owned by the Participant (subject to such terms and conditions, if any, as may be determined by the Administrator); (iii) by shares of Common Stock withheld upon exercise but only if and to the extent that payment by such method does not result in variable accounting or other accounting consequences deemed unacceptable to the Corporation; (iv) in the event that a Public Market (as defined in the Plan) for the Common Stock exists, by delivery of written notice of exercise to the Corporation and delivery to a broker of written notice of exercise and irrevocable instructions to promptly deliver to the Corporation the amount of sale or loan proceeds to pay the Option Price; (v) by such other payment methods as may be approved by the Administrator and which are acceptable under applicable law; or (vi) by any combination of the foregoing methods. Shares delivered or withheld in payment of the Option Price shall be valued at their Fair Market Value on the date of exercise, determined in accordance with the terms of the Plan.

4. No Right of Employment or Service; Forfeiture of Option. Neither the Plan, this Agreement nor any other action related to the Plan shall confer upon the Participant any right to continue in the employment or service of the Corporation or an Affiliate or interfere with the right of the Corporation or an Affiliate to terminate the Participant’s employment or service at any time. Except as otherwise expressly provided in the Plan or this Agreement or as determined by the Administrator, all rights of the Participant with respect to the Option shall terminate upon termination of the employment of the Participant with the Corporation or an Affiliate.

5. Termination of Service. Unless the Administrator determines otherwise (subject to any requirements imposed under Code Section 409A), the Option may be exercised only to the extent vested and exercisable on the Participant’s Termination Date (unless the termination was for Cause), and must be exercised, if at all, prior to the first to occur of the following, as applicable: (a) the close of the period of three years next succeeding the Termination Date; or (b) the close of the Option Period. If the services of a Participant are terminated for Cause, his or her Option shall lapse and no longer be exercisable as of his or her Termination Date, as determined by the Administrator.

6. Nontransferability of Option. The Option shall not be transferable (including by sale, assignment, pledge or hypothecation) other than by will or the laws of intestate succession, except as may be permitted by the Administrator in a manner consistent with the registration provisions of the Securities Act of 1933, as amended (the “Securities Act”). Except as may be permitted by the preceding sentence, the Option shall be exercisable during the Participant’s lifetime only by him or her or by his or her guardian or legal representative. The designation of a beneficiary in accordance with the Plan does not constitute a transfer.

7. Superseding Agreement; Binding Effect. This Agreement supersedes any statements, representations or agreements of the Corporation with respect to the grant of the Option or any related rights, and the Participant hereby waives any rights or claims related to any such statements, representations or agreements. This Agreement does not supersede or amend any existing confidentiality agreement, nonsolicitation agreement, noncompetition agreement, employment agreement or any other similar agreement between the Participant and the Corporation, including, but not limited to, any restrictive covenants contained in such agreements. This Agreement shall be binding upon and shall inure to the benefit of the parties hereto and their respective executors, administrators, heirs, successors and assigns.

8. Governing Law. Except as otherwise provided in the Plan or herein, this Agreement shall be construed and enforced according to the laws of the State of Delaware, without regard to the conflict of laws provisions of any state, and in accordance with applicable federal laws of the United States.

9. Amendment and Termination; Waiver. Subject to the terms of the Plan, this Agreement may be modified or amended only by the written agreement of the parties hereto. The waiver by the Corporation of a breach of any provision of the Agreement by the Participant shall not operate or be construed as a waiver of any subsequent breach by the Participant. Notwithstanding the foregoing, the Administrator shall have unilateral authority to amend the Plan and this Agreement (without Participant consent) to the extent necessary to comply with applicable law or changes to applicable law (including but in no way limited to Code Section 409A, Code Section 422 and federal securities laws).

10. No Rights as Stockholder. The Participant and his or her legal representatives, legatees and distributees shall not be deemed to be the holder of any Shares subject to the Option and shall not have any rights of a stockholder unless and until certificates for such Shares have been issued and delivered to him or her or them.

11. Withholding; Tax Matters.

(a) The Participant acknowledges that the Corporation shall require the Participant to pay the Corporation in cash the amount of any tax or other amount required by any governmental authority to be withheld and paid over by the Corporation to such authority for the account of the Participant, and the Participant agrees, as a condition to the grant of the Option and delivery of the Shares or any other benefit, to satisfy such obligations. Notwithstanding the foregoing, the Corporation may establish procedures to permit the Participant to satisfy such obligations in whole or in part, and any other local, state, federal, foreign or other income tax obligations relating to the Option, by electing (the “election”) to have the Corporation withhold shares of Common Stock from the Shares to which the Participant is entitled. The number of Shares to be withheld shall have a Fair Market Value as of the date that the amount of tax to be withheld is determined as nearly equal as possible to (but not exceeding) the amount of such obligations being satisfied. Each election must be made in writing to the Administrator in accordance with election procedures established by the Administrator.

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(b) The Participant acknowledges that the Corporation has made no warranties or representations to the Participant with respect to the tax consequences (including, but not limited to, income tax consequences) related to the transactions contemplated by this Agreement, and the Participant is in no manner relying on the Corporation or its representatives for an assessment of such tax consequences. The Participant acknowledges that there may be adverse tax consequences upon acquisition or disposition of the Shares subject to the Option and that the Participant should consult a tax advisor prior to such exercise or disposition. The Participant acknowledges that he or she has been advised that he or she should consult with his own attorney, accountant, and/or tax advisor regarding the decision to enter into this Agreement and the consequences thereof. The Participant also acknowledges that the Corporation has no responsibility to take or refrain from taking any actions in order to achieve a certain tax result for the Participant.

12. Administration. The authority to construe and interpret this Agreement and the Plan, and to administer all aspects of the Plan, shall be vested in the Administrator, and the Administrator shall have all powers with respect to this Agreement as are provided in the Plan. Any interpretation of the Agreement by the Administrator and any decision made by it with respect to the Agreement is final and binding.

13. Notices. Except as may be otherwise provided by the Plan or determined by the Administrator, any written notices provided for in this Agreement or the Plan shall be in writing and shall be deemed sufficiently given if either hand delivered or if sent by fax or overnight courier, or by postage paid first class mail. Notices sent by mail shall be deemed received three business days after mailed but in no event later than the date of actual receipt. Notices shall be directed, if to the Participant, at the Participant’s address indicated on Schedule A (or such other address as may be designated by the Participant in a manner acceptable to the Administrator), or, if to the Corporation, at the Corporation’s principal office, attention Chief Financial Officer, Targacept, Inc. Notice may also be provided by electronic submission, if and to the extent permitted by the Administrator.

14. Severability. The provisions of this Agreement are severable and if any one or more provisions may be determined to be illegal or otherwise unenforceable, in whole or in part, the remaining provisions shall nevertheless be binding and enforceable.

15. Restrictions on Option and Shares. The Corporation may impose such restrictions on the Option and the Shares or other benefits underlying the Option as it may deem advisable, including without limitation restrictions under the federal securities laws, the requirements of any stock exchange or similar organization and any blue sky, state or foreign securities laws applicable to such Option or Shares. Notwithstanding any other provision in the Plan or the Agreement to the contrary, the Corporation shall not be obligated to issue, deliver or transfer shares of Common Stock, to make any other distribution of benefits, or to take any other action, unless such delivery, distribution or action is in compliance with all applicable laws, rules and regulations (including but not limited to the requirements of the Securities Act). The Corporation may cause a restrictive legend to be placed on any certificate for Shares issued pursuant to the exercise of the Option in such form as may be prescribed from time to time by applicable laws and regulations or as may be advised by legal counsel.

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16. Effect of Changes in Status. Unless the Administrator, in its sole discretion, determines otherwise (or unless required by Code Section 409A), the Option shall not be affected by any change in the terms, conditions or status of the Participant’s service, provided that the Participant continues to be in the service to the Corporation or an Affiliate. Without limiting the foregoing, the Administrator has sole discretion to determine, subject to Code Section 409A, at the time of grant of the Option or at any time thereafter, the effect, if any, on the Option if the Participant’s status as a Director changes.

17. Right of Offset. Notwithstanding any other provision of the Plan or the Agreement, the Corporation may reduce the amount of any payment otherwise payable to or on behalf of the Participant by the amount of any obligation of the Participant to the Corporation that is or becomes due and payable and the Participant shall be deemed to have consented to such reduction.

18. Counterparts; Further Instruments. This Agreement may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument. The parties hereto agree to execute such further instruments and to take such further action as may be reasonably necessary to carry out the purposes and intent of this Agreement.

[Signatures of the Corporation and the Participant follow on Schedule A/Grant Notice.]

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TARGACEPT, INC.

2006 STOCK INCENTIVE PLAN

Nonqualified Stock Option Agreement

(Nonemployee Directors)

Schedule A/Grant Notice

1. Pursuant to the terms and conditions of the Corporation’s 2006 Stock Incentive Plan, as amended or restated and as it may be hereafter amended or restated (the “Plan”), you (the “Participant”) have been granted an option (the “Option”) to purchase              shares (the “Shares”) of our Common Stock as outlined below.

2. By my signature below, I, the Participant, hereby acknowledge receipt of this Grant Notice and the Option Agreement (the “Agreement”) dated                      , 20    , between the Participant and Targacept, Inc. (the “Corporation”) which is attached to this Grant Notice. I understand that the Grant Notice and other provisions of Schedule A herein are incorporated by reference into the Agreement and constitute a part of the Agreement. By my signature below, I further agree to be bound by the terms of the Plan and the Agreement, including but not limited to the terms of this Grant Notice and the other provisions of Schedule A contained herein. The Corporation reserves the right to treat the Option and the Agreement as cancelled, void and of no effect if the Participant fails to return a signed copy of the Grant Notice within 30 days of grant date stated above.

Note: If there are any discrepancies in the name or address shown above, please make the appropriate corrections on this form. Please retain a copy of the Agreement, including this Grant Notice, for your files.

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