Grenville was the son of George Grenville, a British prime minister. He was, with one interval, a member of parliament from 1780 to 1810, and for a few months during 1806 and 1807 president of the board of control and First Lord of the Admiralty, but is perhaps more famous as a book-collector than as a statesman; he bequeathed his large and valuable library to the British Museum.