He is numbered as the fifth of that name in the Griffith family of the Cefn Amwlch estate, Penllech, now in Gwynedd.
Griffith was returned as Whig Member of Parliament for Caernarvonshire in succession to his brother at a by-election on 27 April 1715.
During the Sunderland Administration from 1717 to 1720, he may have joined the Whig Opposition like his electoral ally, Thomas Wynn.
His son was still a minor when Griffith died on 6 June 1739, and this ended his family's representation of the county in Parliament.
This article about a Member of the Parliament of Great Britain (1707–1800) representing a Welsh constituency is a stub.