McNair was offered a full scholarship to the University of Florida to play defensive back but wanting to play quarterback. McNair played college football for Alcorn State University in the NCAA. In 1992, McNair threw for 3,541 yards and 29 touchdowns, and ran in for 10 more scores. The Braves went 7–4. McNair helped Alcorn State to another good year in 1993, as the Braves upped their record to 8–3 while McNair threw for more than 3,000 yards and 30 touchdowns. 