BAE Systems said the ship's power and propulsion systems are among systems that will be tested and evaluated over a three-week period off the coast of Scotland.
"This is the sixth Type 45 destroyer to embark on sea trials but there will be no complacency in the rigor with which we will put her through her paces and prove her outstanding capabilities," said Paul Rafferty, Type 45 program director at BAE Systems.
The HMS Duncan is to be handed over to the navy in the first half of next year.
The ship is 500 feet long, 67.9 feet in the beam and displaces more than 8,000 tons. It has a range of 7,000 nautical miles at 18 knots and is equipped with air defense missiles.
The ship was built at BAE's Scotstoun shipyard in Scotland and will be based in Portsmouth where BAE Systems will continue to provide ship support.