He was the second son of Richard Grenville and Hester Temple, afterwards Countess Temple, his elder brother being Richard Grenville-Temple, 1st Earl Temple. George received his education at Eton College and at Christ Church College, Oxford, and was called to the bar in 1735. He entered parliament in 1741 as member for Buckingham, and continued to represent that borough till his death.
In parliament he subscribed to the "Boy Patriot" party which opposed Sir Robert Walpole. In December 1744 he became a lord of the admiralty in the administration of Henry Pelham. He allied himself with his brother Richard, and with William Pitt the Elder (Richard's brother-in-law) in forcing their leader to give them promotion by rebelling against his authority and obstructing business. In June 1747 Grenville became a lord of the treasury, and in 1754 treasurer of the navy and privy councillor.
As treasurer of the navy in 1758 he introduced and carried a bill which established a fairer system of paying the wages of seamen. He remained in office in 1761, when his brother the Earl of Chatham resigned upon the question of the war with Spain, and in the administration of Lord Bute functioned as leader of the House of Commons. In May 1762 he was appointed Secretary of State for the Northern Department, and in October First Lord of the Admiralty; and in April 1763 he became first lord of the treasury and Chancellor of the Exchequer.
Prominent measures of his administration included the prosecution of John Wilkes and the passing of the American Stamp Act (1765), which led to the first symptoms of alienation between America and the Great Britain. During the latter period of his term of office he was on a very unsatisfactory footing with the young king George III, who gradually came to feel a kind of horror of the interminable persistency of his conversation, and whom he endeavoured to make use of as the mere puppet of the ministry. The king made various attempts to induce Pitt to come to his rescue by forming a ministry, but without success, and at last had recourse to the Marquis of Rockingham. When Rockingham agreed to accept office, the king dismissed Grenville (July 1765). He never again held office.
The nickname of "gentle shepherd" was given him because he bored the House by asking over and over again, during the debate on the Cider Bill of 1763, that somebody should tell him "where" to lay the new tax if it was not to be put on cider. Pitt whistled the air of the popular tune Gentle Shepherd, tell me where, and the House laughed. Though few excelled him in a knowledge of the forms of the House or in mastery of administrative details, he lacked tact in dealing with people and with affairs.
In 1749 he married Elizabeth, daughter of Sir William Wyndham, by whom he had a large family. His son, George Grenville, 2nd Earl Temple, was created Marquess of Buckingham, and his grandson was Richard Temple-Nugent-Brydges-Chandos-Grenville, 1st Duke of Buckingham and Chandos. Another son was William, afterwards Lord Grenville. Another son was Thomas Grenville, the MP and book-collector.
The Grenville Papers, being the Correspondence of Richard Grenville, Earl Temple, K.G., and the Right Hon. George Grenville, their Friends and Contemporaries, were published at London in 1852, and afford the chief authority for his life. But see also Horace Walpole's Memoirs of the Reign of George II (London, 1845); Lord Stanhope's History of England (London, 1858); Lecky's History of England (1885); and ED Adams, The Influence of Grenville on Pitt's Foreign Policy (Washington, 1904).