Trombonist Henry Coker was born in Dallas on December 24, 1919. As a child Coker lived in Omaha for a time. He began his formal musical training in high school at Washington, Texas, where he studied the piano and harp. He continued with these instruments into his early college career. While studying music at Wiley College in Marshall, Texas, he developed an interest in jazz that led him to switch to the trombone. Inspired by the music of Duke Ellington and others, Coker first worked regularly in the jazz field in 1935 with the band of trumpeter John White. He was with Nat Towles's band from 1937 to 1939. During this period he began to create for himself a highly distinctive solo style. Abruptly, however, he left the jazz world behind, darting off to Honolulu to play in a series of Hawaiian bands, including a period with drummer Monk McFay.
On returning to the United States in 1945, Coker became a member of Benny Carter's band in California. He later joined the Eddie Heywood Sextet to go on a tour that included important dates in New York City. He stayed with Heywood until 1947. During his time with Heywood he recorded with a number of jazz artists, among them fellow trombonist Vic Dickenson. After leaving the Heywood Sextet Coker remained on the West Coast freelancing and doing studio work until 1949, when he joined the Illinois Jacquet band. Illness forced him to leave Jacquet around 1950. After he recovered, his consequent financial difficulties ended when he landed a job with the Count Basie Orchestra in 1952. Coker so impressed Basie that he was assigned the post of section leader and principal trombone soloist. During his long tenure with the Basie band (1952–63) Coker had countless opportunities for solos on such songs as "No Name," "Redhead," and "Peace Pipe." He also was the principal trombone soloist on the important retrospective album The Count Basie Story (1960). Coker spent much of his later career doing studio work in New York City and playing with the Ray Charles orchestra, with which he remained from 1966 through 1971. For most of the 1970s he worked as a freelance and studio musician in the Los Angeles area. He played on the soundtrack for the movie Lady Sings the Blues (1972), and for four months in 1973 he was back with the Count Basie band. He also was reunited briefly with Ray Charles in 1976.
Coker's career thus featured performances with some of the most important jazz groups from the 1930s to the mid-1970s. His longest and most notable engagement was with the Count Basie Orchestra. He was well-known for his forceful, imposing musical style, which was mirrored by his massive frame and commanding personality. He was also a musical perfectionist, as his impressive solos demonstrate. He is especially notable for his ability to combine his roots in 1930s-era swing with more modern, improvisational jazz methods. Deliberate, forceful attacks and inventive, technically conscious solos personified Coker's style. His playing possessed a rugged vitality, and owing to this and to his reputation as a self-critic, Coker is regarded as an important jazz trombonist. He died in Los Angeles on November 23, 1979.