Randy Grimes was an American football player who played center for the Tampa Bay Buccaneers from 1983 to 1992. Randy played for Baylor University during the early 1980s and was a part of the 1980 Southwest Conference Champion Bears, which also included the likes of other NFL players Mike Singletary, Alfred Anderson, Mark Kirchner, Vic Vines, Walter Abercrombie, and Vann McElroy.