Alexander Craig attended the University of Melbourne, where he graduated with a Bachelor of Arts with Honours, and a Diploma of Education. He served in New Guinea, Cape York and Thursday Island with the A.I.F. from 1942-1946. After the war, he became Senior English Master at Mount Scopus College in Victoria. In the 1990s he was a co-presenter of the Sunday lunchtime jazz program broadcast on Sydney's 2MBS FM
Craig's poetry has been published in anthologies, and in Australian and international literary journals, such as Meanjin, Poetry, Southerly and Voices.