He was born around 1739, the son of Archibald Dickson. He initially entered the merchant navy in 1752. He moved to the
Royal Navy in 1755 and passed the lieutenant exam in 1759. In 1765, he was given command of , and in 1771, he took command of
HMS Thunder. Promoted to
captain on 31 January 1774, Dickson was given command of the
fourth-rate in January 1774 and the
sixth-rate in October 1775. In Greyhound, he took part in the
action against the Penobscot Expedition in July 1779 and fought at the
Battle of Martinique in April 1780 during the
American Revolutionary War. After that, he was given command of the third-rate in 1786, of the third-rate in 1790, and of the third-rate in 1793. In August 1800, a diplomatic mission was sent to
Copenhagen under
Lord Whitworth, accompanied by a fleet under Dickson's command. He was promoted to full
admiral on 1 January 1801, ==Baronetcy and death==