Robert Grant was born in Bombay on 10 August 1837, the son of Sir Robert Grant, Governor of Bombay, and his wife Margaret, daughter of Sir David Davidson. He joined the Royal Artillery and Royal Engineers and in 1857 was sent to Jamaica. He became aide-de-camp to Lieut-General Sir William Fenwick Williams in North America for six years before returning to Aldeshot. He was promoted to Captain in July 1867 and Major in 1872. At the War Office he was deputy assistant adjutant-general for the Royal Engineers, and held subsequent posts at Plymount, Woolwich and Edinburgh. He was sent to Egypt to serve with Lord Wolseley and the Nile expeditionary force but was invalided home after catching fever. He was mentioned in dispatches for his services. On 18 April 1851 he was appointed Inspector-General of Fortifications. He was promoted K.C.B on 20 May 1896 and given the G.C.B. on 26 June 1902. He died on 8 January 1904.

On 24 November 1875 he married Victoria Alexandrina, daughter of John Cotes of Woodcote Hall, Shropshire; they had twin sons, both of whom were in the army, and a daughter who died young. A replica of the present paitning, painted in 1897, is in the collection of the Royal Engineers.