Grachan Moncur III (June 3, 1937 – June 3, 2022) was an American jazz trombonist. He was the son of jazz bassist Grachan Moncur II and the nephew of jazz saxophonist Al Cooper.

Born in New York City, United States, (his paternal grandfather was from the Bahamas) and raised in Newark, New Jersey, Grachan Moncur III began playing the cello at the age of nine, and switched to the trombone when he was 11. In high school, he attended the Laurinburg Institute in North Carolina, the private school where Dizzy Gillespie had studied. While still at school, he began sitting in with touring jazz musicians on their way through town, including Art Blakey and Jackie McLean, with whom he formed a lasting friendship.

After high school, Moncur toured with Ray Charles (1959–62), Art Farmer and Benny Golson‘s Jazztet (1962), and Sonny Rollins. He took part in two Jackie McLean albums for Blue Note in 1963, One Step Beyond and Destination… Out!, to which he also contributed the bulk of compositions. He recorded two albums of his own for Blue Note, Evolution (1963) with Jackie McLean and Lee Morgan, and Some Other Stuff (1964) with Herbie Hancockand Wayne Shorter.