Jimmy Simpson (October 6, 1897 – August 7, 1979) was a blocking back in the National Football League. Simpson first played with the Toledo Maroons during the 1922 NFL season. The following season, he was a member of the St. Louis All-Stars, but did not see any playing time during a regular-season game. He played with the Kenosha Maroons during his final season after the Toledo Maroons made the move from Toledo, Ohio to Kenosha, Wisconsin.