Graham played bass in the highly successful and influential funk band Sly and the Family Stone from 1967 to 1972. Upon the band's disintegration due to lead singer Sly Stone's drug addiction, Graham formed his own band, Graham Central Station, which had some success through the 1970s. The name is a pun of "Grand Central Station", a famous train station located in the Manhattan borough of New York City.

In the early 1980s, Graham had several solo hits. His biggest hit was "One in a Million You," which reached number 9 on the Billboard chart in 1980.

He recorded another album in the late 1990s with a new band using the Graham Central Station name.

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