Sultan Mahmud was born on 29 April 1930 in Kuala Terengganu. He was married to Sharifah Nong Fatima As-Saggoff binti Sayyid Abdullah As-Saggoff and Tengku Ampuan Bariah binti Almarhum Sultan Sir Hisamuddin Alam Shah, sister of late Sultan Selangor, Almarhum Sultan Salahuddin Abdul Aziz Shah in 1951. He was a cousin to the late Almarhum Sultan Salahuddin Abdul Aziz Shah of Selangor.