Nunn was born in Pittsburgh, Pennsylvania to William G. Nunn, Sr., a well-known journalist and editor at the Pittsburgh Courier, as well as an NFL scout. Nunn's paternal grandfather was the first African American football player at George Westinghouse High School. Nunn attended Morehouse College in Atlanta, Georgia.

Nunn made his acting debut in the 1988 Spike Lee film School Daze, and is perhaps best remembered for his roles as Radio Raheem in Lee's Do the Right Thing and as Nino Brown's verbally challenged bodyguard Duh Duh Duh Man in New Jack City.

Some of his other film credits include Lee's Mo' Better Blues and He Got Game, as well as Regarding Henry, Sister Act, The Last Seduction, Things To Do In Denver When You're Dead, New Jack City, Runaway Jury, Spider-Man trilogy, and the television series The Job.