Admiral Barrington was a ship built in 1781 in France and was employed as a French West Indiaman, though under a different name.

At the time of Admiral Barrington's first voyage for the EIC, her principal managing owner was Godfrey Thornton.

On her return trip to Britain she reached Macao on 7 January 1788, Saint Helena on 22 April, and Deptford on 1 August.

[3] Under the command of Robert Abbon Mash, she sailed from Portsmouth, England, on 27 March 1791 as part of the third fleet and arrived in Port Jackson, New South Wales on 16 October.

She brought with her Captain William Paterson,[6] three noncommissioned officers, and 24 privates of the New South Wales Corps.

[6] Originally, before she left for Botany Bay, her captain's intent was to go to China to pick up a back-haul cargo for the EIC.