Born in Bradford, Yorkshire, Stevens' first introduction to painting was assisting his father in his work as a signwriter. From 1952-57, he studied at Bradford Regional College of Art, forming friendships with fellow students including David Hockney, David Oxtoby, Michael Vaughan, and John Loker. Stevens moved to London in 1957 to study painting at the Royal College of Art; his tutors included Ceri Richards.
After graduating, Stevens taught at art schools in Hornsey, Maidstone and Manchester, and in 1974-75, he was the Gregory Fellow at Leeds University. After this, however, Stevens gave up teaching to focus on his art. In 1975, he won the Chichester Arts Festival Prize, and in 1983, he received a John Moore's Exhibition award. He also exhibited internationally and in 1976, a major exhibition of his work was held at the V&A, London.
Stevens began printmaking in 1970, and soon had an international reputation for his technical skill and ability as a printmaker, even mastering difficult techniques such as mezzotint. Prints of gardens and trees are considered a speciality of Stevens, particularly the studies of Kew and Kensington Gardens. Stevens exhibited his prints across Europe, including a British Council Touring Exhibition of Scandanavia (1977) and the Bilbao Print Biennale (1982), as well as regularly exhibiting at the British International Print Biennale in Bradford, where he won prizes in 1979 and 1982.
In 1987, Stevens was elected a Royal Academician but unfortunately died the following year. Retrospectives of Stevens' work were held at the Redfern Gallery in 1989 and 2003. He is represented in the collections of the Arts Council, Tate, and the V&A.
"Norman Anthony Stevens was a 'Yorkshireman'. Raised amid the gritty disciplined austerity of a post-war northern mill town. A youth crippled with polio carrying a justifiable chip and a will to fight the world. He became a man of substantial strength, aggressively tough, a powerful character, possessed of an abrasively sharp and ready wit coupled with a wry sense of humour. Though he could be most disarmingly charming his deeply emotional and sensitive nature was invariably well controlled. Interwoven with the many facets of his personality was the 'northern work ethic', life was an art piece for Norman, be it building fireplaces, tending flowers, cooking or making prints, each and every task was completed to the best of his abilities. He had a desire to help others which made him an excellent organiser, valued art teacher, loving family man, confidant, associate and loyal friend. His contribution to the arts and artists was immeasurable. He will be sadly missed but joyously remembered. I loved Norman as a friend from the age of twelve and find it difficult to envisage life without him."
David Oxtoby, The Guardian, 1988