Grachan Moncur III (born June 3, 1937) is an American jazz trombonist. He is 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 the early 1960s, 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 Hancock and Wayne Shorter.

Moncur joined Archie Shepp‘s ensemble, and recorded with other avant-garde players such as Marion Brown, Beaver Harris and Roswell Rudd (another free jazz trombonist). During a stay in Paris in the summer of 1969, he recorded two albums as a leader for the BYG Actuel label, New Africa and Aco Dei de Madrugada, as well as appearing as a sideman on other releases of the label. In 1974, the Jazz Composer’s Orchestra commissioned him to write Echoes of Prayer (1974), a jazz symphony featuring a full orchestra plus vocalists and jazz soloists. His sixth album as a leader, Shadows (1977) was released only in Japan. Unfortunately, he was subsequently plagued by health problems and copyright disputes and recorded only rarely. Through the 1980s, he recorded with Cassandra Wilson (1985), played occasionally with the Paris Reunion Band and Frank Lowe, appeared on Big John Patton‘s Soul Connection (1983), but mostly concentrated on teaching. In 2004, he re-emerged with a new album, Exploration, on Capri Records featuring Moncur’s compositions arranged by Mark Masters for an octet including Tim Hagans and Gary Bartz.