1741-1818. He was born on 9 December 1741 at Graemeshall, Holm, on the Orkney Islands, the third son of Mungo Graeme and his wife Jean Chancellor.
On 17 December 1760 he was commissioned lieutenant of the Temple 68, Captain Lucius O Brien, seeing service in the Leeward Islands and moving to the Aquilon 28, Captain Chaloner Ogle, on the same station on 17 March 1762. After a brief visit to Newfoundland under Captain Philip Perceval he went on half pay in September 1763 when she was paid off at the peace.
He was briefly aboard the Portsmouth guardships Thunderer 74, Captain Samuel Hood, from September 1764 until the end of March 1765, and then the Superb 74, Captain Robert Hathorn, from April to October 1765. In October 1765 he was appointed to command the snow Egmont 10 with the rank of lieutenant, going out to Newfoundland in the summer of 1767 and also seeing service off Ireland before leaving her in July 1770. From January 1774 he served aboard the Preston 50, Captain John Robinson, flying the flag of Vice-Admiral Samuel Graves in North America.
Although promoted commander on 9 September 1775 and appointed to the Viper 10 in North American waters, he did not join her but instead held the temporary command of the Mercury 20 from November 1775, transporting Major-General Sir Henry Clinton and several companies of grenadiers from Boston to Sandy Hook for conferral with loyalist groups in the following January. He thereafter commanded the sloop Kingfisher 18 from February 1776, serving under the orders of Captain Henry Bellew of the Liverpool 28 off the Delaware Capes in the summer and in the occupation of Rhode Island on 8 December 1776. In May 1777 he was stationed in the Seaconnet Passage in North America, being attached to Vice-Admiral Lord Howe s command, and in August was at Boston under the orders of Captain Charles Fielding of the Diamond 32.
He was posted captain of the Sphinx 20 on 24 January 1778, conveying troops from Rhode Island to Cape Cod in May, and he was present during the fleet manoeuvres off Rhode Island in August 1778. When the fleet returned to Rhode Island from New York to find that the French had left the Sphinx moved in and bombarded the rebel positions around Rhode Island on 29 August.
He next held the command of the Diamond 32 in succession to Captain Charles Fielding, joining Commodore William Hotham s small squadron that was despatched from North America at the beginning of November to reinforce Rear-Admiral Hon. Samuel Barrington at Barbados. This frigate was not present at the defence of St. Lucia on 15 December 1778 however, and that winter Graeme exchanged with Captain John Linzee into the Pearl 32 which he brought home to pay off in the spring of 1779.
He recommissioned the Tartar 28 in July 1779, serving in the controversial Commodore George Johnstone s squadron, and off Cape Finisterre on 11 November he was sent in chase of the Spanish frigate Santa Margarita 28, Captain Don Andrea de Viana. He quickly received her surrender after she fell aboard the Tartar and carried away her mizzen topsail yard, although the presence of the remainder of Johnstone s squadron undoubtedly convinced the enemy of the impracticability of further flight. The Spanish frigate was bought into the navy under her own name. Graeme continued to serve off Portugal with Johnstone, and after capturing the Infanta Carlotta on 2 September 1780 he eventually left the Sphinx after arriving at Portsmouth from Lisbon in February 1781.
In March 1781 he recommissioned the Preston 50, serving in the North Sea and fighting at the Battle of the Doggersbank on 5 August 1781, where he lost an arm in the action, and where his ship suffered total casualties of ten men killed and forty wounded. He immediately went on half-pay at the start of the following month and was not re-employed for a further thirteen years, during which time he succeeded his elder brother Patrick to the family estates.
Graeme was appointed to command the Glory 98 in the Channel from January 1795, but in February had to race back to Scotland to comfort his dying mother. He was promoted rear-admiral on 1 June 1795, vice admiral on 14 February 1799, and during that summer was appointed commander-in-chief at the Nore. Flying his flag in the Zealand 64, Captain Thomas Parr, and from June 1800 Captain William Mitchell, he held this position until the resumption of hostilities in April 1803, his flag lieutenant throughout this period being William Pryce Cumby
On 23 April 1804 he was advanced to the rank of admiral, and he died at Edinburgh on 5 August 1818, being buried at Greyfriars Church in the city.
Graeme never married, and on his death the family estate passed to a distant relative in Jamaica whom he had never met.