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 September 30, 2020, 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 Marc Grasso, M.D., as Chief Financial Officer and Chief Business Officer 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 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.

This certification accompanies the Form 10-Q to which it relates, is not deemed filed with the Securities and Exchange Commission and is not to be incorporated by reference into any filing of Kura Oncology, Inc. under the Securities Act of 1933, as amended, or the Securities Exchange Act of 1934, as amended (whether made before or after the date of the Form 10-Q), irrespective of any general incorporation language contained in such filing.

/s/ Troy E. Wilson, Ph.D., J.D.	/s/ Marc Grasso, M.D.
Troy E. Wilson, Ph.D., J.D.	Marc Grasso, M.D.
President and Chief Executive Officer	Chief Financial Officer and Chief Business Officer
Date: November 5, 2020	Date: November 5, 2020