As with others in her class she was loosely modeled on the design and dimensions of HMS Tartar, launched in 1756 and responsible for capturing five French privateers in her first twelve months at sea.

[1] Admiralty contracts for Griffin's construction were issued to commercial shipwright Moody Janverin of Bursledon on 16 May 1757, with a stipulation that work be completed within twelve months.

The choice of name followed a trend initiated in 1748 by John Montagu, 4th Earl of Sandwich, in his capacity as First Lord of the Admiralty, of using figures from classical antiquity as descriptors for naval vessels.

[6][7] She was also built with broad and heavy masts, which balanced the weight of her hull, improved stability in rough weather and made her capable of carrying a greater quantity of sail.

[9][c] Among these other ranks were four positions reserved for widow's men – fictitious crew members whose pay was intended to be reallocated to the families of sailors who died at sea.