Born in West Kensington, London, he studied at Birmingham College of Art from 1941 to 1943 where he was taught still-life drawing and painting by Bernard Fleetwood-Walker RA. He was subsequently conscripted into the Royal Air Force and trained as aircrew flying Wellingtons and then Liberators. After the War he won a place at the Royal College of Art, graduating in 1951. He returned there to teach in the printmaking department in 1955 becoming head of department in 1970 and Professor in 1984.
Despite his academic focus on printmaking, Alistair Grant is as well-known as a painter as he is a printmaker, being elected to, and regularly exhibiting at, the London Group and the Royal Society of British Artists. He also regularly exhibited at the Royal Academy. Examples of his work can be found in numerous public collections, including the Victoria and Albert Museum and the Government Art Collection.