Granville was the eldest son of Bernard Granville (1631–1701) (4th son of Sir Bevil Grenville (1596–1643) who died in heroic circumstances at the Battle of Lansdowne), Master of the Horse and a Gentleman of the Bedchamber to King Charles II (1660–1685) and MP for Launceston, Saltash, Lostwithiel and Plymouth, by his wife Anne Morley, daughter and sole heiress of Cuthbert Morley of Hornby, Yorkshire. His uncle was John Granville, 1st Earl of Bath (1628–1701), of Stowe, Kilkhampton in Cornwall, who played a prominent role in the Restoration of the Monarchy of 1660. His family was descended from Sir Richard I de Grenville (d. post 1142) (alias de Grainvilla, de Greinvill, etc.), one of the Twelve Knights of Glamorgan, of Neath Castle, Glamorgan and of Bideford, Devon and Stowe, Kilkhampton in Cornwall. In 1661 the family changed the spelling of its surname from Grenville to Granville, to emphasise its supposed origins at Granville, Normandy.
After keeping his terms at Trinity College, Cambridge, he was awarded Master of Arts in 1679. He then obtained a commission in the regiment of foot nominally commanded by his uncle, John Granville, 1st Earl of Bath (1628–1701). He received the honour of knighthood from King James II (1685–1688). He was engaged in military action in the Low Countries. In December 1693 he came over from Flanders, waited on King William III, of whom he seems to have been a favourite, and gave him an account of the state of that country.
In January 1694 he was gazetted to the colonelcy of the regiment of the Earl of Bath, on the latter's resignation, and joined it in Flanders. In Flanders in June 1695, in consequence of a violent quarrel, he fought a duel with Colonel the Marquis de Rada, who shortly afterwards died of his wounds. On 21 March 1695–6 he was appointed by the king Governor of Pendennis Castle in Cornwall. At the end of May he re-embarked for Flanders, where again he got into trouble, "being accused by several officers for illegal practices on his regiment". A court-martial, however, acquitted him. In June 1698 his regiment was ordered to Ireland . In May 1702 Granville accepted the governorship of Barbados, with a salary of £2,000 per annum, but did not sail for the colony until March 1703. He had scarcely settled when he fell dangerously ill of a fever which had spread across the island. Some of the planters complained to the privy council of his tyranny and extortion. After a full hearing on 20 July 1705, Grenville was "honourably acquitted", but it was deemed politic to recall him in the following year of 1706. He died at sea on his passage home in September or October 1706.
He died at sea on his passage home from Barbados in September or October 1706. He was unmarried. By his will, dated 16 January 1701-2, and proved at London on 6 November 1706, he left his estate to his brother, George Granville, later created Baron Lansdowne