Admiral Barrington was built in 1781 in France and was employed as a French West Indiaman, though under a different name. She was captured in 1782 and was later sold to Godfrey Thornton. Thornton renamed her Admiral Barrington. She then made one full voyage for the East India Company (EIC) from 1787 till 1788. Her most notable voyage was as a convict ship in the third fleet to Australia. On her return voyage in 1793 pirates attacked her near Bombay and murdered almost her entire crew. She was apparently recovered, only to have a French privateer capture her in the West Indies in 1797. The privateer took her to Bordeaux, where she was sold.