Francis Greville was the eldest son of Fulke Greville, 5th Baron Brooke and Sarah Dashwood.

He married Lady Anne Wilmott, daughter and eventual coheiress of John Wilmot, 2nd Earl of Rochester

John Wilmot, 2nd Earl of Rochester

John Wilmot, 2nd Earl of Rochester , styled Viscount Wilmot between 1652 and 1658, was an English Libertine poet, a friend of King Charles II, and the writer of much satirical and bawdy poetry. He was the toast of the Restoration court and a patron of the arts...

 (who was the widow of Henry Baynton). They had two sons:

• Fulke Greville, 6th Baron Brooke (1693–1711)
• William Greville, 7th Baron Brooke (1695–1727)

Francis served as Member of Parliament

Member of Parliament

A Member of Parliament is a representative of the voters to a :parliament. In many countries with bicameral parliaments, the term applies specifically to members of the lower house, as upper houses often have a different title, such as senate, and thus also have different titles for its members,...

 for Warwick

Warwick (UK Parliament constituency)

Warwick was a parliamentary borough consisting of the town of Warwick, within the larger Warwickshire constituency of England. It returned two Members of Parliament to the House of Commons of England from 1295 to 1707, to the House of Commons of Great Britain from 1707 to 1800, and then to the...

 from 1695 until his death (though not between 1698 and 1701). He predeceased his father and his barony passed direct to his eldest son.