Exhibit 5.1

Charles J. Bair

(858) 550-6142

cbair@cooley.com

April 17, 2015

Kura Oncology, Inc.

11119 N. Torrey Pines Road, Suite 125

La Jolla, CA 92037

Ladies and Gentlemen:

You have requested our opinion with respect to certain matters in connection with the filing by Kura Oncology, Inc., a Delaware corporation (the “Company”), of a Registration Statement on Form S-1 (the “Registration Statement”) with the Securities and Exchange Commission, including a related prospectus filed with the Registration Statement (the “Prospectus”), covering the registration for resale of up to 14,279,820 shares (the “Shares”) of the Common Stock, $0.0001 par value, of the Company on behalf of selling stockholders.

In connection with this opinion, we have examined and relied upon the Registration Statement, the Prospectus, the Company’s Amended and Restated Certificate of Incorporation, and Amended and Restated Bylaws, and the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. We have assumed the genuineness and authenticity of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies thereof and the due execution and delivery of all documents where due execution and delivery are a prerequisite to the effectiveness thereof.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares are validly issued, fully paid and nonassessable.

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to the Registration Statement.

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