He was born in 1782 in West Alvington, Devon, the eldest son of Sir Alexander Grant, 7th Baronet and Sarah Cray. He graduated from St John's College, Cambridge in 1806 with a Master of Arts (MA). He entered politics in Jamaica, where he owned two plantations, as a member of the Jamaican colonial assembly from 1810 to 1811. In 1812, he returned to England where he successfully stood as a Tory Member of Parliament for Tregony in the House of Commons. In 1818, he was elected as MP for Lostwithiel, and was re-elected there in June 1826, although he was also elected to Aldborough which he chose to represent instead. From 1826 to 1831, Grant was the Chairman of Ways and Means in the House of Commons. He was unsuccessful in elections for Grimsby in 1835, and Honiton, but re-entered the House representing Cambridge in 1840, until 1843.
Grant succeeded his father as Baronet of Dalvey upon the latter's death in 1825. Grant himself died in London on 29 November 1854 aged 72, and was succeeded in the baronetcy by his brother, Robert Innes Grant.