Born in London on 27 Aug 1886, eldest of the three sons of the Rev. Dr James Gow (1854-1923), fellow of Trinity College, Cambridge and headmaster of Nottingham high school and later of Westminster School, and his wife, Gertrude Sydenham Everett-Green (1855-1942). He was grandson of the historian Mary Anne Everett Green (1818-1895), and nephew of novelist Evelyn Everett-Green; also, which may have been significant for his interest in the visual arts, of watercolourist Mary Lightbody Gow (1851-1929), and Keeper of the Royal Academy Andrew Gow (1848-1928), whose circle included Poynter and Alma-Tadena and after whom he was christened. He was educated at Nottingham high school, at Rugby School, and at Trinity College, Cambridge, to which he went with a classical scholarship in 1905. While a student, he won numerous prizes, and obtained first classes in both parts of the classical tripos (1908 and 1909), with a distinction in classical archaeology. He, along with Justin Brooke, Rupert Brooke, and Hugh Wilson, helped found the Marlowe Dramatic Society. He began a systematic study of early French, Italian, Dutch and Flemish painting in 1910, visiting galleries abroad in spring or autumn, sometimes both. He won a Trinity prize fellowship in 1911, and took on pupils, but though he applied several times for permanent teaching posts in Cambridge he was unsuccessful; he therefore, after a term at Winchester College, became a master at Eton College and remained there through the First World War, being disqualified for military service by a heart murmur.
He returned to Trinity and resumed his fellowship in 1925 as college and university lecturer, becoming tutor in 1929 and serving as praelector from 1946-1951. He served in turn on the Council of the Senate and on the Faculty General Board, and was chairman of the Board of Fine Arts. He was Brereton Reader of Classics at Cambridge from 1947-1951, and was awarded honorary degrees from Durham and Edinburgh universities. He published a large number of articles for 1913, many on Theocritus, of whose collected works he published a highly-regarded edition in 1950. He followed this in 1952 with an edition of the other Greek bucolic poets, publishing a translation with notes of the work in 1953; in the same year he and his friend A. F. Scholfield brought out an edition of the Hellenistic didactic poet Nicander. Later, his work concentrated on the epigrams of the Hellenistic Greek Anthology, and he published an edition of the "Garland of Meleager" in 1965 and the "Garland of Philip" in 1968, in collaboration with Denys Page.
He was a syndic of the Fitzwilliam Museum from 1934 to 1957, and his collection of works by Degas, Rodin and Forin was left to it in his will. To the National Gallery, of which he was a trustee from 1947 to 1953, he left the collection of photographs of paintings which, along with his personal library of books on art, did much to stimulate the interest of undergraduates; they often visited him in the evening to socialise. Despite his dry and severe manner, many students greatly profited from his teaching and company, and the monthly circular letter he wrote to pupils on active service during the Second World War, published in 1945 as "Letters from Cambridge", reveal the warm heart and sense of humour known by his friends. His senior colleague A. E. Housman, shortly before his death in 1936, paid tribute to him: "No one could have a better friend than I have found in Gow".
Gow published a thoughtful and revealing memoir of Housman, acted as his literary executor, and supervised a reprint of his edition of Manilius. Other friends included the classical archaeologist and art historian John Beazley, and George Orwell, whose tutor at Eton he was.
Gow enjoyed fishing, royal tennis, and skating, until impaired health in later life precluded them. He died on 2 February 1978.