Exhibit 3.1

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.”

* * *

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.