His most successful year came in 1987 when he won the Greater Greensboro Open and his only major the U.S. Open. In 1989 Scott won the BellSouth Atlanta Golf Classic. He won the GTE Byron Nelson Golf Classic in 1993 and the Buick Invitational in 1998. Simpson also won the Walker Cup in 1977 for the United States. He finished 6th at the PGA Championship in both 1984 and 1993 and 7th at the 1990 Masters Tournament. He started playing senior golf in 2005 and won his first Champions Tour title in 2006.