John Tunnard was born in Sandy, Bedfordshire, and educated at Charterhouse School. He studied design at the Royal College of Art (1919–1923). In 1926, he married a fellow student, Mary May Robertson.
During the 1920s he worked in various textile design jobs in Manchester — for Tootal, Broadhurst, Lee & Co, the carpet manufacturers, H&M Southwell, and John Lewis Partnership. He took up painting seriously in 1928, and taught design at the Central School of Arts and Crafts, London, from 1929.
In 1931 he exhibited at the Royal Academy and with the London Group, which he joined in 1934. In 1933 the Tunnards moved to Cadgwith, Cornwall, where they ran a business making printed silks. From the mid-1930s, he became friends with Julian Trevelyan, Henry Moore, John Betjeman and Humphrey Spender.
During World War II he considered himself a conscientious objector, although, as no man born earlier than 1 July 1900 was required for call-up, an occasion for formally registering his objection never arose. Nevertheless, feeling morally obliged to make a contribution, he worked briefly as a fisherman in 1939, then as an auxiliary coastguard for the duration of the war.
From 1945 to 1965 he taught at the Penzance School of Art. He exhibited again at the Royal Academy in 1960, and was elected as an Associate in 1967. He died in Penzance in 1971.