Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the reference to our firm under the caption “Experts” in this Registration Statement (Form S-3) and related Prospectus of Kura Oncology, Inc. for the registration of up to $200,000,000 of common stock, preferred stock, debt securities, and warrants and to the incorporation by reference therein of our report dated March 5, 2019, with respect to the financial statements of Kura Oncology, Inc. included in its Annual Report (Form 10-K) for the year ended December 31, 2018, filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

August 1, 2019