Graham's career began in New Orleans selling art in the French Quarter. He has painted many local figures, such as Alton Ochsner, Sr. His mural "The Good Earth Forever" was hung at the Terrebonne General Medical Center in Houma and unveiled by then governor Edwin Edwards.
Graham regularly enters art shows around the country. His paintings and pastels were well received and won Best Show in several top shows, including the American Artist Professional League, the Salmagundi Open, and the Knickerbocker Artists show. He won the Southern Artist Award from the Allied Artists Show for a pastel of a New Orleans denizen entitled "The Veteran." In 1990, he was given the title of Master Pastellist by the Pastel Society of America.