Crawford Mims (March 21, 1933 to April 21, 2001) is an American former college football player who was an All-American guard for the Ole Miss Rebels football team of the University of Mississippi. Mims attended the University of Mississippi in Oxford, Mississippi starting in 1950, where he played coach Johnny Vaught's Ole Miss Rebels football team from 1951 to 1953. During his three seasons as a Rebel, the team compiled an overall win-loss-tie record of 21–6–4. As a junior lineman for the 8–0–2 Rebels in 1952, he played in the Sugar Bowl on January 1, 1953. The 1952 rebels finished No. 7 in both the final AP Poll and Coaches Poll.