Exhibit 23.2

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the Registration Statement (Form S-8) pertaining to the 2018 Equity Incentive Plan, the 2018 Employee Stock Purchase Plan and the 2004 Stock Plan of Sutro Biopharma, Inc. of our report dated June 1, 2018 (except for the third paragraph of Note 1 and for Note 14, as to which the date is September 17, 2018), with respect to the financial statements of Sutro Biopharma, Inc. for the years ended December 31, 2016 and 2017, included in the Registration Statement (Form S-1 No. 333-227103) filed with the Securities and Exchange Commission.

/s/ Ernst & Young LLP

Redwood City, California

September 26, 2018