MRCS Eng LRCP Edin 1878.
Graham studied medicine at Owens College Manchester and Paris, he was senior house surgeon at Royal Berkshire Hospital Reading before being appointed senior resident medical officer at Royal Manchester Children's Hospital. Graham returned to Wigan where he was a general practitioner for over forty years. He was also honorary surgeon and later consultant surgeon at the Royal Albert Edward Infirmary. Graham was president of the Wigan Medical Society and was on the council of the Lancashire and Cheshire Branch of the BMA. Graham retired in 1919 to Bolton-le-Sands and died on 27 April 1924 aged sixty seven. His son, Charles Lester Graham, and his daughter, Florence Muriel Louise Graham (later Holt), also went into medical practice.