A gritty fighter who made the most of his potential, Grant turned pro in 1984 as a light heavyweight and lost to Henry Tillman in his second pro fight. In 1986 he defeated Matthew Saad Muhammad but was never really able to hit a groove. He looked headed towards a journeyman status, and dropped a series of fights, including a decision to Bobby Czyz in 1990. In 1991 he lost to Frank Tate, and moved up to cruiserweight. In 1993 he landed a shot at IBF Cruiserweight Title holder Alfred Cole and lost a decision. In 1995 Grant landed a rematch with Cole and lost another decision. The next year Grant was outboxed by a young Chris Byrd over 10 rounds. Rather than give up, in 1997 Grant earned a shot at IBF Cruiserweight Title holder Adolpho Washington and won a close decision, winning his only title. The success was short lived, and Grant lost the belt in his next fight to unheralded Imamu Mayfield.
Grant had a resurgence in 2000 when he shockingly TKO'd legendary but aging Thomas Hearns in the 2nd round. It was short lived, and in 2002 Grant stepped up to heavyweight and took on Brian Nielsen and lost a decision. Grant dropped back down to cruiser, but failed to win another fight, including losses to Rydell Booker in 2003 and Eliecer Castillo in 2004. Grant hasn't fought since the loss to Castillo.