Brown attended Delaware State College and Maryland State College and played in Philadelphia before joining, first, Tadd Dameron (Dameron, Tadd)'s band in Atlantic City, N.J., then Lionel Hampton (Hampton, Lionel)'s big band for a European tour, both in 1953. He then played with leading West Coast musicians and the Art Blakey (Blakey, Art) quintet. In 1954 he and drummer Max Roach (Roach, Max) formed the Brown-Roach quintet, which quickly became one of the outstanding postwar jazz units. Brown and Richie Powell, the quintet's pianist, died in an accident on the Pennsylvania Turnpike.

From 1953, when Brown began recording frequently, his style was fully mature. Influenced by Fats Navarro (Navarro, Fats), he developed an innate sense of solo form, a rich tone, and a virtuoso technique in all trumpet ranges. His style included brilliant high notes, high rhythmic detail, and a generous incorporation of grace notes and varied inflections, all of which he played with rare grace and ease. He was especially noted for the melodic qualities of his improvising, which often flowed in long phrases. Most of his recordings are of consistently high quality, at his best in the Brown-Roach At Basin Street and Sonny Rollins Plus Four albums (both 1956). The jazz standard “Joy Spring” (1954) is one of the best-known songs that he wrote.

Brown was the most influential trumpeter of his generation; the lyrical aspects of his music influenced many trumpeters, including Lee Morgan (Morgan, Lee) and Booker Little, and his technical brilliance especially influenced trumpeters such as Donald Byrd and Freddie Hubbard.