He was promoted to be a lieutenant in the navy on 7 May 1755, and served at that rank on board the 60-gun Eagle from 1755 to 1757,[1] the 100-gun HMS Royal George when she carried Lord Anson's flag in the summer of 1758, and under Sir Edward Hawke in 1759.

These dates seem to throw great doubt on the accuracy of Charnock's statement that, on 24 June 1759, Griffith married the widow of Lord George Bentinck, who died on 1 March 1759.

After watching it carefully, he despatched full intelligence to Hawke and to the Admiralty, while he himself went to warn Admiral Thomas Brodrick, then blockading Cadiz.

His conduct on this occasion called forth an unusually warm encomium from the admiralty, as well as a direct intimation that 'he might very soon expect some mark of their favour' (Minute on Griffith's official letter of 17 November 1759).

When John Byron resigned the command to Rear-Admiral Hyde Parker, Griffith was moved into the 74-gun HMS Conqueror; but a few months later, on 18 December 1779, was killed in a slight encounter with the French in Fort Royal Bay, the Battle of Martinique.