Washington Bullets (1988–1993)

Selected twelfth overall by the Washington Bullets in the 1988 NBA draft out of Oklahoma, Grant averaged 5.6 points, 2.3 rebounds and 1.1 assists per game. He lifted his averages to 8.2 points, 4.2 rebounds and 1.6 assists the following season, in 1989–90. Grant improved markedly in the 1990–91 campaign, when he averaged 18.2 points, 7.2 rebounds, 2.6 assists and 1.18 steals per game. At season's end, he was runner-up to the 1991 NBA Most Improved Player Award (which was earned by Orlando's Scott Skiles). In two subsequent seasons, he continued his solid play with 18.0 and 18.6 points per contest in 1991–92 and 1992–93, respectively.

Portland Trail Blazers (1993–1996)

In 1993, Grant was traded to the Portland Trail Blazers in exchange for center Kevin Duckworth, where he was instead utilized in a secondary role off the bench, and in three seasons with Portland, averaged 9.6 points per game.

Return to Washington (1996–1998)

On July 15, 1996, Grant returned to the Washington Bullets via a trade, along with Blazers point guard Rod Strickland, for power forward Rasheed Wallace and shooting guard Mitchell Butler. By this stage Grant's career was on a downslide, averaging 4.1 points in 1996–97, then slipping to 2.6 points the following season when the Bullets franchise had reinvented itself as the Wizards.

Philadelphia 76ers (1999)

Grant rounded out his professional career with the Philadelphia 76ers in the lockout-shortened 1999 NBA season, averaging 3.1 points and 2.3 rebounds in 47 of 50 possible games.

Grant was traded just before the 1999–00 season along with Anthony Parker to the Orlando Magic for Billy Owens, who had previously been sent to the Magic in a trade that sent brother Horace to the Seattle SuperSonics. He subsequently was waived by the team and retired from the league afterwards.

Never proficient as a rebounder in comparison with his brother, he holds career averages of 4.4 rebounds and 9.9 points per game.