Famous as both a professional football player and an Olympic sprinter, Graddy played for the Denver Broncos and the Los Angeles Raiders during the late 1980s and early 1990s and won a team gold medal in the 4 x 100 meter event at the 1984 Summer Olympics in Los Angeles, California.
In 1983, while attending the University of Tennessee, he won a gold medal with his national relay team at the Pan American Games and also won an NCAA title with his collegiate track team.
He set a personal record in the sixty meter event at a 1985 race in Paris, France, and recorded his best time in the one hundred meter dash at a 1984 track meet in Knoxville, Tennessee.
He spent his early days in Gaffney, South Carolina, and his high school years in Atlanta, Georgia.
He and fellow track star Carl Lewis both won gold medals at the 1984 Olympics. In the 100 meter dash event, Graddy won silver and Lewis won gold.