Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the inclusion in this Registration Statement on Form S-1 of Compass Therapeutics, Inc. of our report dated June 23, 2020 on our audits of the financial statements of Compass Therapeutics LLC and Subsidiary as of December 31, 2019 and 2018 and for the years then ended. We also consent to the reference to our firm under the heading “Experts.”

/s/ CohnReznick LLP

Roseland, New Jersey

August 6, 2020