SECOND AMENDMENT TO THE CANCER PREVENTION PHARMACEUTICALS, INC. 2010 EQUITY INCENTIVE PLAN

Exhibit 4.13

SECOND AMENDMENT TO THE

CANCER PREVENTION PHARMACEUTICALS, INC.

2010 EQUITY INCENTIVE PLAN

This Second Amendment to the Cancer Prevention Pharmaceuticals, Inc. 2010 Equity Incentive Plan (the “Plan”) is effective September 27, 2012.

WHEREAS, the Board of Directors of Cancer Prevention Pharmaceuticals, Inc., a Delaware corporation (the “Company”) has adopted and the stockholders of the Company have approved the Plan, as amended; and

WHEREAS, the Board of Directors deems it to be in the best interest of the Corporation to amend the Plan in order to increase the maximum number of shares of common stock that may be subject to Awards and sold under the Plan from 265,000 shares to 300,000.

NOW, THEREFORE, the Plan shall be amended as follows:

“3(a) Stock Subject to the Plan. Subject to the provisions of Section 11 of the Plan, the maximum aggregate number of Shares that may be subject to Awards and sold under the Plan is 300,000 Shares. The Shares may be authorized but unissued, or reacquired Common Stock.”

IN WITNESS WHEREOF, the undersigned Chairman and Chief Executive Officer of the Company certifies that the foregoing Second Amendment of the Cancer Prevention Pharmaceuticals, Inc. 2010 Equity Incentive Plan was duly adopted by the Board of Directors of the Company.