Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of Kura Oncology, Inc. (the “Company”) for the period ended March 31, 2016, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), Troy E. Wilson, Ph.D., J.D., as President and Chief Executive Officer of the Company, and Heidi Henson, as Chief Financial Officer and Secretary of the Company, each hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to the best of his or her knowledge:

1. the Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ Troy E. Wilson, Ph.D., J.D.	/s/ Heidi Henson
Troy E. Wilson, Ph.D., J.D.	Heidi Henson
President and Chief Executive Officer	Chief Financial Officer and Secretary
Date: May 11, 2016	Date: May 11, 2016