Graham Williams was born in the Adelaide suburb of St Peters, and attended Prince Alfred College.

He worked in Adelaide with the firm Goldsbrough Mort & Co.[2] A tall fast-medium bowler and useful lower-order batsman, Williams had his best season for South Australia in 1937–38, when he took 24 wickets at an average of 24.20 and made 233 runs at 21.18.

[1] Warrant-Officer Navigator Williams was taken prisoner in July 1941 after his plane was shot down over Libya, and was released in April 1945.

[9] Despite having lost 31 kilograms during his imprisonment, less than a month after his release Williams was playing cricket for an RAAF team against an Empire XI at Lord's.

[8] He played for services teams throughout the 1945 season, including all five of the Victory Tests between Australian servicemen and England.