The son of Richard Graves (1677-1729), antiquary of Mickleton, Glos., he became associated with the Oxford Methodists, including George Whitefield, while at Magdalen College. In 1737 his friends abducted him as 'stark mad', but he was befriended by Charles Wesley, who took him to Stanton Harcourt, where John Gambold, another member of the Holy Club, was then vicar. Converted in 1738, he began field-preaching in and around Lady Huntingdon's Donington Park, but in 1740 was persuaded to sign a paper disclaiming his Methodism. Two years later, in August 1742, he renounced this declaration. Meeting him in Bristol in August 1746, John Wesley found him a problematic ally, but in December 1765, just after his ordination to the priesthood, he assisted Wesley at West Street chapel, London.
His older brother, Richard Graves (1715-1804), a graduate of Pembroke College and fellow of All Souls, Oxford, was rector of Claverton, Som. From 1749 to 1804. His literary career included editing, translation and writing, especially poetry and the satirical novel The Spiritual Quixote (published in 1773, but written much earlier), in which he good-humouredly lampooned the enthusiasm of the Methodist field-preachers, and Whitefield in particular.