Born in New York City (his father’s father 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 trombonewhen 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 classic Jackie McLean albums in the early 1960s, One Step Beyond and Destination… Out!, to which he also contributed the bulk of compositions and which led to two influential albums of his own for Blue Note Records, Evolution (1963) with Jackie McLean and Lee Morgan, and Some Other Stuff (1964) with Herbie Hancock and Wayne Shorter.