Church of Scotland minister. Son of George Grant (1700-1772), Minister of Kirkmichael, and Ann Chapman. Married (1782) to Grace Fraser, with whom he had several children. One of their sons, James Grant (1790-1853) became Minister at Nairn, while another, George Grant (b. 1787) became a merchant in Liverpool.
Alexander Grant was educated at King's College, Aberdeen, from where he graduated M.A. in 1759. He spent some years as a missionary at Fort William from 1764, before becoming minister of the Parish of Daviot and Dunlichity near Inverness on April 2, 1771. He was translated to the nearby Parish of Cawdor in 1779 upon the death of its previous minister Kenneth Macaulay.
Boswell and Dr Johnson met Alexander Grant at the Manse of Cawdor on August 27, 1773, as they stayed there for the night as guests of Kenneth Macaulay, the local minister. Boswell described him as "an intelligent and well-bred minister". According to Boswell, Grant told them "a story of an apparition, which he had from the Rev. Mr Grant at Nigg, who saw it.". Later, Dr Johnson went with Grant to see their host's library, which Johnson thought "rather a lady’s library, with some Latin books in it by chance." In the evening, Grant said prayer, and he and Boswell slept in the same room for the night, while Dr Johnson had a room for himself.1
Grant joined them again at Mr Keith's in Inverness on the 29th, where he had tea with them, and he and Keith supped with them at their inn in the evening.