Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in this Registration Statement on Form S-8 of Compass Therapeutics, Inc. of our report dated June 23, 2020 on our audits of the consolidated financial statements of Compass Therapeutics LLC and Subsidiary as of December 31, 2019 and 2018 and for the years then ended.

/s/ CohnReznick LLP

Parsippany, New Jersey

January 13, 2021