After graduating from Miami Senior High School, Grant became an All-City first-team selection and Player-of-the-Year played at the University of Dayton from 1983 to 1987 while residing at 3 Evanston (The Gateway) and guiding them to the Elite Eight of the NCAA Tournament before bowing out to eventual national champion Georgetown. As a sophomore, Grant averaged 10.7 points a game and 6.5 rebounds a game and the Flyers again made it to the NCAA Tournament. As a junior, the 6'5" Grant moved from power forward to small forward and averaged 7.1 points a game and 4.8 rebounds a contest while the team advanced to the National Invitation Tournament. As a senior, Grant was named a team captain awarded team MVP and the Sharpenter Memorial Rebounding Award after leading the squad in scoring and rebounding, averaging 13.0 and 6.0 respectively. In his 105 appearances, Grant registered 11.6 points and 6.7 rebounds each time out. In 1987, Grant spent a year playing for the Miami Tropics of the United States Basketball League.