Julian Otto Trevelyan was born on 20 February 1910, the son of poet and translator Robert Calverley Trevelyan (1872-1951) and his Dutch wife Elizabeth, née des Amorie van der Hoeven (1975-1957). He attended Bedales School and was admitted to Trinity College Cambridge in 1928, where he spent two years reading English but did not complete his degree; he was linked to the modernist group associated with the magazine Experiment, which included William Empson, Jacob Bronowski, Humphrey Jennings, and Kathleen Raine. He first exhibited work with the London Group in 1929. In 1931 he moved to Paris to pursue an artistic career, working first at the Académie Moderne run by Fernand Léger and Amédée Ozenfant, and then with Stanley Hayter at Atelier 17 where he met Miró and Picasso. He was friends with fellow-artists such as Alexander Calder, Anthony Gross (1905-84), and Maria Helena Vieira da Silva. His first joint exhibition, with Robin Darwin, was at the Bloomsbury Gallery in London in 1932.
After his return to England in 1935 he made his home at Durham Wharf on the Thames, where he lived for the rest of his life. His first one-man show was held that year at the Lefèvre Galleries, and some of his paintings and etchings were chosen for the 1936 International Surrealist Exhibition at the New Burlington Galleries in London. In 1937-1938, he worked for Tom Harrisson's Mass-Observation movement, producing landscape collages of newspaper scraps, ephemera, and coloured paper. He helped organize the 'Unprofessional Painting' exhibition of works by amateur artists, which was shown at Gateshead-upon-Tyne and Peckham in autumn 1938, also participating in a debate on 'Painting and Realism' with amateur artists from the Ashington Group of Nottingham miners. He attended pacifist demonstrations and produced work in support of the Republicans during the Spanish Civil War (1936-39). At the outbreak of the Second World War he joined Hayter's Industrial Camouflage Research Unit with his friend Roland Penrose, before serving as a camouflage officer with the Royal Engineers from 1940 until he was invalided out in 1943.
From 1950 to 1960 he taught etching at the Chelsea School of Art and at the Royal College of Art from 1955 to 1963. In 1963 he suffered a viral infection of the brain which permanently affected his speech and caused him to give up teaching. He concentrated thereafter on printmaking, and in 1965 was one of the founder members of the Printmakers' Council, though he later resumed painting as well. He was made a senior fellow of the Royal College of Art and an honorary senior Royal Academician in 1986.
Trevelyan travelled widely, making visits to Mount Athos (in 1931), Yugoslavia (in 1932), where he worked as part of a small film unit and painted murals in Dubrovnik, Malta (in 1958 and again in 1970), Russia (in 1960), Uganda (in 1966), India (1967-68), Morocco (in 1972), and to most countries in Europe. Several of his 'suites' of prints were inspired by these travels. In 1934 he married the potter Ursula Darwin; they had one son, Philip Erasmus (b 1943), but divorced in 1949. In 1951 he married the artist Mary Fedden, who survived him at his death on 12 July 1988.