Falconer was the son of a barber in Edinburgh, where he was born. He became a sailor, and thereby competent to describe the management of a storm-tossed vessel, whose career and fate are told in his poem, The Shipwreck (1762), a work of genuine, if unequal talent. Falconer's efforts to improve the poem in a later edition were not wholly successful. The work won him the patronage of the Duke of York, through whose influence he was appointed purser on various warships. He had been one of three survivors of a trading ship on a voyage from Alexandria to Venice. In 1751 Falconer produced a poem on the death of Frederick, Prince of Wales. He also contributed poems to the Gentleman's Magazine. The Shipwreck was dedicated to the then rear-admiral the Duke of York. Falconer was briefly a midshipman on the Royal George, then in 1763, he became purser of the frigate Glory, aboard which he wrote the political satire Demagogue. In 1767 he was the purser of the Swiftsure. In 1769 he published An Universal Dictionary of the Marine. William Falconer was a passenger in the frigate Aurora when it was lost at sea on a voyage to India. He was last seen on 24 December 1769.