He started as a clerk in a bank. He was in the military during the First World War. He got rheumatic fever during this time, and had it his whole life. He entered the British Museum in 1921 where he worked for Charles Tate Regan (1878-1943). From 1939 to 1944, he was in charge of the Natural History Museum at Tring. Norman wrote "A History of Fishes" (1931) and "A Draft Synopsis of the Orders, Families and Genera of Recent Fishes" (1957).