Graham was born in Kansas City, Missouri in September 1918 and grew up in Denver, Colorado, where he led his own ensemble which included Paul Quinichette among its members.
He worked with Count Basie, Lucky Millinder, Herbie Fields, and Erskine Hawkins early in his career.
Following his employment with Gillespie he led his own band in New York City, in addition to touring Europe with Sarah Vaughan in 1953.
From 1955 to 1957, he was back with Basie, including on the 1956 release April in Paris and the Newport Jazz Festival.
Outside of jazz, Graham also played on numerous R&B recordings, including on those of Wynonie Harris, Joe Williams, and Little Willie John.