He was the third, but eldest surviving, son and heir of Admiral Adam Duncan, 1st Viscount Duncan of Camperdown, and the former Henrietta Dundas. His father was a well known British admiral who defeated the Dutch fleet off Camperdown in what is considered one of the most significant actions in naval history. His father had been created a peer of Great Britain by George III in 1797. Duncan was an Ensign in the Coldstream Guards in 1797. He succeeded his father on 4th August 1804 as the 2nd Viscount Duncan of Camperdown and 20th Laird of Gleneagles. He was Grand Master of Scottish Freemasons from 1812 to 1814.