Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statement on Form S-1 filed pursuant to Rule 462(b) of the Securities Act of 1933 of the reference to our firm under the caption “Experts” and “Risk Factors” and to the incorporation by reference of our report dated May 4, 2018 (except for the second paragraph of Note 2, as to which the date is September 21, 2018), with respect to the financial statements of Gritstone Oncology, Inc. included in Amendment No. 2 to the Registration Statement (Form S-1 No. 333-226976) and related Prospectus of Gritstone Oncology for the registration of its common stock.

/s/ Ernst & Young LLP

Redwood City, California

September 24, 2018