Thompson sailed to the West Indies commanding , the flagship of Vice-Admiral William Parry, and later moved to the frigate . He returned to England in 1774, and then went back to the West Indies in command of in early 1776 (capturing the 20-gun French ship "Le Compas"). He accompanied a merchant convoy to England in October 1777, before yet again going out to the West Indies in 1780. Sir John Laforey was appointed commissioner of the shipyard at Antigua in 1780, but Thompson refused to recognize this authority, leading to a long feud. In the Caribbean, Thompson was moved by Sir George Rodney to the 74-gun , commanding her throughout the American War of Independence, including at the battles of the Chesapeake, St Kitts, under Sir Samuel Hood). In April 1782, Thompson was present in the rear division at the Battle of the Saintes. Sir George Rodney's decisive victory over the French in the Caribbean. He sailed "Alcide" back to England at the end of the War.