Exhibit 3.1

RESTATED CERTIFICATE OF INCORPORATION

OF

CURIS, INC.

CURIS, INC. (the “Corporation”), a corporation organized and existing under and by virtue of the General Corporation Law of the State of Delaware (the “General Corporation Law”), hereby certifies as follows:

The name of the Corporation is Curis, Inc. A Certificate of Incorporation of the Corporation was filed with the Secretary of State of the State of Delaware on February 14, 2000.

This Restated Certificate of Incorporation restates and integrates and further amends the Certificate of Incorporation of the Corporation, was duly adopted by the Board of Directors of the Corporation in accordance with the provisions of Sections 141 and 245 of the Delaware General Corporation Law, and was approved by written consent of the stockholders of the Corporation given in accordance with the provisions of Section 228 and Section 242 of the Delaware General Corporation Law (prompt notice of such action having been given to those stockholders who did not consent in writing).

The text of the Certificate of Incorporation of the Corporation is hereby restated and amended to read in its entirety as follows:

FIRST: The name of this corporation (the “Corporation”) is Curis, Inc.

SECOND: The address of the registered office of the Corporation in the State of Delaware is 1209 Orange Street, Wilmington, Delaware 19801, County of New Castle, and the name of its registered agent at such address is The Corporation Trust Company.

THIRD: The purpose for which the Corporation is organized is to engage in any lawful act or activity for which corporations may be organized under the General Corporation Law of the State of Delaware.

FOURTH: The Corporation is authorized to issue two classes of capital stock, one of which is designated as common stock, $.01 par value per share (“Common Stock”), and the other of which is designated as preferred stock, $.01 par value per share (“Preferred Stock”). The total number of shares of both classes of capital stock that the Corporation shall have authority to issue is 130,000,000 shares, consisting of 125,000,000 shares of Common Stock and 5,000,000 shares of Preferred Stock. The Preferred Stock may be issued from time to time in one or more series as set forth in Section (b) of this Article FOURTH. The following is a statement of the designations and the powers, preferences and rights of, and the qualifications, limitations or restrictions applicable to, each class of capital stock of the Corporation.

(1) General. The voting, dividend and liquidation rights of holders of Common Stock are subject to and qualified by the rights of holders of Preferred Stock of any series as may be designated in any resolution or resolutions providing for the issue of such series as may be adopted by the board of directors as hereinafter provided.

(2) Voting. Holders of Common Stock are entitled to one vote for each share held at all meetings of stockholders. The number of authorized shares of Common Stock may be increased or decreased (but not below the number of shares thereof then outstanding) by the affirmative vote of the holders of a majority of the capital stock of the Corporation entitled to vote, irrespective of the provisions of Section 242(b)(2) of the General Corporation Law of the State of Delaware.

(3) Dividends. Dividends may be declared and paid on Common Stock from funds lawfully available therefor, as and when determined by the board of directors and subject to any preferential dividend rights of any series of Preferred Stock then outstanding.

(4) Liquidation. Upon the dissolution or liquidation of the Corporation, whether voluntary or involuntary, holders of Common Stock will be entitled to receive all assets of the Corporation available for distribution to stockholders of the Corporation, subject to any preferential rights of any series of Preferred Stock then outstanding.

(1) Issuance. Preferred Stock may be issued from time to time in one or more series, each of which series shall have such terms as are set forth herein and in any resolution or resolutions providing for the issue of such series as may be adopted by the board of directors as hereinafter provided. Any shares of Preferred Stock that may be redeemed, purchased or acquired by the Corporation may be reissued except as otherwise expressly provided in this Certificate of Incorporation or provided by law. Different series of Preferred Stock shall not be construed to constitute different classes of capital stock for the purposes of voting by classes unless expressly provided.

(2) Authority of Board. Authority is hereby expressly granted to the board of directors to provide for the issuance of Preferred Stock from time to time in one or more series, and in connection with the creation of any such series, to determine and fix such voting powers, full or limited, or no voting powers, and such designations, preferences and relative participating, optional or other special rights thereof, and qualifications, limitations or restrictions applicable thereto, as shall be stated and expressed in such resolutions, all to the full extent now or hereafter permitted by the General Corporation Law of the State of Delaware. Without limiting the generality of the foregoing, a resolution or resolutions providing for issuance of any series of Preferred Stock may provide for dividend rights, conversion rights, redemption privileges and liquidation preferences applicable to such series and may provide that such series shall rank superior, equal or junior to the Preferred Stock of any other series, in each case except as otherwise expressly provided in this Certificate of Incorporation or as provided by law. Except as otherwise provided in this Certificate of Incorporation, no vote of holders of Common Stock or holders of Preferred Stock shall be a prerequisite to the designation or issuance of any shares of any series of Preferred Stock authorized by and complying with the conditions of this Certificate of Incorporation.

FIFTH: Special meetings of stockholders may be called at any time by the Chairman of the Board, the Chief Executive Officer (or if there is no Chief Executive Officer, the President) or the board of directors. Business transacted at any special meeting of stockholders shall be limited to matters relating to the purpose or purposes stated in the notice of the general meeting. From and after the effective date of the Form 8-A Registration Statement under the Securities

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Exchange Act of 1934, as amended, the stockholders of the Corporation shall not be permitted to take any action otherwise required to be taken at any annual meeting or special meeting of the stockholders of the Corporation by a consent in writing in lieu of any such meeting.

SIXTH: No director shall be personally liable to the Corporation or to any of its stockholders for monetary damages arising out of such director’s breach of fiduciary duty as a director of the Corporation, except to the extent that the elimination or limitation of such liability is not permitted by the General Corporation Law of the State of Delaware, as the same exists or may hereafter be amended. No amendment to or repeal of the provisions of this Article SIXTH shall deprive any director of the Corporation of the benefit of the provisions of this Article SIXTH with respect to any act or failure to act of any director occurring prior to such amendment or repeal.

SEVENTH: In furtherance of and not in limitation of powers conferred by statute, it is further provided that:

Subject to the limitations and exceptions, if any, contained in the by-laws of the Corporation, the by-laws may be adopted, amended or repealed by the board of directors.

Elections of directors need not be by written ballot unless otherwise provided in the by-laws of the Corporation.

Subject to any applicable requirements of the General Corporation Law of the State of Delaware, the books of the Corporation may be kept outside the State of Delaware at such location or locations as may be designated from time to time by the board of directors or in the by-laws of the Corporation.

EIGHTH: The Corporation shall indemnify each person who was or is a party or is threatened to be made a party to any threatened, pending or completed action, suit or proceeding, whether civil, criminal, administrative or investigative (other than an action by or in the right of the Corporation), by reason of the fact that such person is or was, or has agreed to become, a director or officer of the Corporation, or is or was serving or has agreed to serve, at the request of the Corporation, as a director, officer or trustee of, or in a similar capacity with, another corporation (including any partially or wholly owned subsidiary of the Corporation), partnership, joint venture, trust or other enterprise (including any employee benefit plan), against expenses (including attorneys’ fees), judgments, fines and amounts paid in settlement actually and reasonably incurred in connection with any such action, suit or proceeding to the maximum extent permitted by the General Corporation Law of Delaware. The foregoing right of indemnification shall in no way be exclusive of any other rights of indemnification to which any such director or officer may be entitled, under any by-law, agreement, vote of directors or stockholders or otherwise. No amendment to or repeal of the provisions of this paragraph shall deprive a person of the benefit of this paragraph with respect to any act or failure to act of such person occurring prior to such amendment or repeal.

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NINTH: Whenever a compromise or arrangement is proposed between the Corporation and its creditors or any class of them or between the Corporation and its stockholders or any class of them, any court of equitable jurisdiction within the State of Delaware may, on the application in a summary way of the Corporation or of any creditor or stockholder thereof or on the application of any receiver or receivers appointed for the Corporation under Section 291 of Title 8 of the Delaware Code or on the application of trustees in dissolution or of any receiver or receivers appointed for the Corporation under Section 279 of Title 8 of the Delaware Code, order a meeting of the creditors or class of creditors, and/or of the stockholders or class of stockholders of the Corporation, as the case my be, to be summoned in such manner as the said court directs. If a majority in number representing three-fourths in value of the creditors or class of creditors, and/or of the stockholders or class of stockholders of the Corporation, as the case may be, agree to any compromise or arrangement and to any reorganization of the Corporation as a consequence of such compromise or arrangement, the said compromise or arrangement and the said reorganization shall, if sanctioned by the court to which the said application has been made, be binding on all the creditors or class of creditors, and/or on all the stockholders or class of stockholders, of the Corporation, as the case may be, and also on the Corporation.

TENTH: The Corporation reserves the right to amend, alter, change or repeal any provision contained in this Certificate of Incorporation in the manner now or hereafter prescribed by the General Corporation Law of the State of Delaware and this Certificate of Incorporation, and all rights conferred upon stockholders herein are granted subject to this reservation. Notwithstanding any provision of law, any other provision of this Certificate of Incorporation or any provision of the by-laws of the Corporation, the affirmative vote of the holders of three-fourths of the shares of capital stock of the Corporation issued and outstanding and entitled to vote shall be required to amend or repeal, or to adopt any provision inconsistent with, any provision of Article FIFTH or this Article TENTH.

ELEVENTH: The name of the sole incorporator of the Corporation is Jonathan H. Hulbert and his mailing address is c/o Foley, Hoag & Eliot LLP, One Post Office Square, Boston, Massachusetts 02109.

IN WITNESS WHEREOF, the Corporation has caused this Restated Certificate of Incorporation to be executed by the undersigned as of the 16^th day June, 2000.

CERTIFICATE OF AMENDMENT

OF

RESTATED CERTIFICATE OF INCORPORATION

OF

CURIS, INC.

Curis, Inc. (the “Corporation”), a corporation organized and existing under and by virtue of the General Corporation Law of the State of Delaware, does hereby certify:

FIRST: That the Board of Directors of the Corporation has duly adopted resolutions authorizing and approving an amendment to the Restated Certificate of Incorporation of the Corporation to (i) increase the number of authorized shares of capital stock of the Corporation and (ii) increase the number of authorized shares of Common Stock of the Corporation.

SECOND: That the amendment to the Restated Certificate of Incorporation of the Corporation set forth in this Certificate of Amendment was duly adopted in accordance with the provisions of Section 242 of the General Corporation Law of Delaware by the Board of Directors and holders of a majority of the outstanding stock of the Corporation entitled to vote thereon.

THIRD: That upon the effectiveness of this Certificate of Amendment, the first paragraph of Article FOURTH of the Restated Certificate of Incorporation is hereby amended and restated as follows:

“FOURTH: The Corporation is authorized to issue two classes of capital stock, one of which is designated as common stock, $.01 par value per share (“Common Stock”), and the other of which is designated as preferred stock, $.01 par value per share (“Preferred Stock”). The total number of shares of both classes of capital stock that the Corporation shall have authority to issue is 230,000,000 shares, consisting of 225,000,000 shares of Common Stock and 5,000,000 shares of Preferred Stock. The Preferred Stock may be issued from time to time in one or more series as set forth in Section (b) of this Article FOURTH. The following is a statement of the designations and the powers, preferences and rights of, and the qualifications, limitations or restrictions applicable to, each class of capital stock of the Corporation.”

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IN WITNESS WHEREOF, this Certificate of Amendment of Restated Certificate of Incorporation has been executed by a duly authorized officer of the Corporation on this 30^th day of May, 2013.