Moore was born in Glasgow, Scotland, the son of Jean Simson and John Moore, doctor and author.
He entered the Navy in 1777 at the age of 13.
He was promoted to lieutenant on 8 March 1782 to serve aboard Crown, taking part in the relief of Gibraltar under Lord Howe, and the subsequent battle of Cape Spartel in October.
During the peace he travelled through France, but was recalled to serve aboard Perseus, Dido, and then Adamant, the flagship of Sir Richard Hughes on the North American Station.
On 22 November 1790 he was promoted to commander in the sloop Bonetta, before finally returning to England in 1793.

Moore was promoted to post-captain on 2 April 1794, soon after the start of the Revolutionary War, with command of the 32-gun frigate Syren, in the North Sea and the coast of France.
He then commanded the 36-gun frigate Melampus from September 1795.
In her he took part in the Battle of Tory Island on 12 October 1798, capturing the French frigate Résolue two days later.
In February 1800 he went out to the West Indies, but was invalided home after eighteen months.

On the renewal of the war in 1803 he was appointed to Indefatigable (44), and with three other frigates — Medusa (32), Lively (38) and Amphion (32) — under his command, captured a Spanish treasure fleet of four frigates — Medea (40), Clara (34), Fama (34) and Mercedes (36) — carrying bullion from the Caribbean back to Spain off Cadiz in the Action of 5 October 1804.

Moore was then attached to Sir Robert Calder's squadron blockading Ferrol.
In 1808, he served as commodore, flying his broad pennant in the new ship Marlborough assisting Admiral Sir Sidney Smith with the Portuguese royal family's escape to Brazil, and was subsequently made a Knight of the Order of the Tower and Sword.

He later served as part of the North Sea fleet for several years.
At the close of the Walcheren campaign in December 1809, he was entrusted with destroying the basin, arsenal, and sea defences of Flushing (Vlissingen).

Moore commanded Chatham from March 1812, until promoted to rear-admiral on 12 August 1812, and served as Commander-in-Chief in the Baltic for a short time, flying his flag in HMS Fame.
In 1814 he served as captain of the fleet to Lord Keith in the Channel, and, having been appointed a Knight Commander of the Order of the Bath on 2 January 1815, he became second-in-command, Mediterranean Fleet in 1815.
He joined the Board of Admiralty as First Naval Lord in the Liverpool ministry in May 1816.

Promoted to vice-admiral on 12 August 1819, he left the Board of the Admiralty in March 1820.
He was Commander-in-Chief, Mediterranean Fleet between 1820 and 1823 and was advanced to Knight Grand Cross of the Order of the Bath on 11 March 1836.
Promoted to full admiral on 10 January 1837, he served as Commander-in-Chief, Plymouth from 1839 to 1842 flying his flag in Impregnable.

Moore died at his home, Brook Farm, Cobham, Surrey, on 25 November 1843, and was buried at St. Andrew's Church.
Moore was born in Glasgow, Scotland, the son of Jean Simson and John Moore, doctor and author. He entered the Navy in 1777 at the age of 13. He was promoted to lieutenant on 8 March 1782 to serve aboard Crown, taking part in the relief of Gibraltar under Lord Howe, and the subsequent battle of Cape Spartel in October. During the peace he travelled through France, but was recalled to serve aboard Perseus, Dido, and then Adamant, the flagship of Sir Richard Hughes on the North American Station. On 22 November 1790 he was promoted to commander in the sloop Bonetta, before finally returning to England in 1793.
Moore was promoted to post-captain on 2 April 1794, soon after the start of the Revolutionary War, with command of the 32-gun frigate Syren, in the North Sea and the coast of France. He then commanded the 36-gun frigate Melampus from September 1795. In her he took part in the Battle of Tory Island on 12 October 1798, capturing the French frigate Résolue two days later. In February 1800 he went out to the West Indies, but was invalided home after eighteen months.
On the renewal of the war in 1803 he was appointed to Indefatigable (44), and with three other frigates — Medusa (32), Lively (38) and Amphion (32) — under his command, captured a Spanish treasure fleet of four frigates — Medea (40), Clara (34), Fama (34) and Mercedes (36) — carrying bullion from the Caribbean back to Spain off Cadiz in the Action of 5 October 1804.
Moore was then attached to Sir Robert Calder's squadron blockading Ferrol. In 1808, he served as commodore, flying his broad pennant in the new ship Marlborough assisting Admiral Sir Sidney Smith with the Portuguese royal family's escape to Brazil, and was subsequently made a Knight of the Order of the Tower and Sword.
He later served as part of the North Sea fleet for several years. At the close of the Walcheren campaign in December 1809, he was entrusted with destroying the basin, arsenal, and sea defences of Flushing (Vlissingen).
Moore commanded Chatham from March 1812, until promoted to rear-admiral on 12 August 1812, and served as Commander-in-Chief in the Baltic for a short time, flying his flag in HMS Fame. In 1814 he served as captain of the fleet to Lord Keith in the Channel, and, having been appointed a Knight Commander of the Order of the Bath on 2 January 1815, he became second-in-command, Mediterranean Fleet in 1815. He joined the Board of Admiralty as First Naval Lord in the Liverpool ministry in May 1816.
Promoted to vice-admiral on 12 August 1819, he left the Board of the Admiralty in March 1820. He was Commander-in-Chief, Mediterranean Fleet between 1820 and 1823 and was advanced to Knight Grand Cross of the Order of the Bath on 11 March 1836. Promoted to full admiral on 10 January 1837, he served as Commander-in-Chief, Plymouth from 1839 to 1842 flying his flag in Impregnable.
Moore died at his home, Brook Farm, Cobham, Surrey, on 25 November 1843, and was buried at St. Andrew's Church.
Graham Moore (Royal Navy officer)