Grant was the son of Captain Grant of Easter Elchies.
He studied law at the University of Edinburgh and was admitted as an advocate on 12 February 1712, and obtained a good practice. On 3 November 1732 he was raised to the bench with the title of Lord Elchies, in succession to Sir John Maxwell of Pollock; on 3 March 1737 he succeeded Walter Pringle, Lord Newhall as a lord of justiciary.
He is buried in the sealed south-west section of Greyfriars Kirkyard in Edinburgh, in the area known as the Covenanter's Prison. His family lie with him.
Family
He married Margaret (1697–1746), daughter of Sir Robert Dickson of Inveresk, Baronet. Their children died young: Barbara (1729–1759), David (1731–1747), Mary (1735–1747).