His father was Sir Richard Grenville, MP; one of his elder brothers was Earl Temple, a government minister.
Another brother, Thomas, was also an MP, and the third, James, was Lord of Trade and Cofferer of the Household.
Another brother, George Grenville, rose to become Chancellor of the Exchequer under William Pitt the Elder and was later Prime Minister himself in 1763–1765.
He was appointed British ambassador to the Ottoman Empire in Constantinople on 1 May 1761, but did not arrive until 21 February 1762.
He left Turkey to return to England on 13 October 1765 to become Commissioner of Customs before retiring to Bath, where he died in 1784.