Grant was born at Nairn, where his father was the parish minister, and educated at the grammar school and Marischal College, Aberdeen. In 1846 he joined the Indian army. He saw active service in the Sikh War (1848—49), served throughout the Indian Mutiny of 1857, and was wounded in the operations for the relief of Lucknow.
He returned to England in 1858, and in 1860 joined John Hanning Speke in the memorable expedition which solved the problem of the Nile sources. The expedition left Zanzibar in October 1860 and reached Gondokoro, where the travellers were again in touch with what they regarded civilization, in February 1863. Speke was the leader, but Grant carried out several investigations independently and made valuable botanical collections. He acted throughout in absolute loyalty to his comrade.
In 1864 he published, as supplementary to Speke's account of their journey, A Walk across Africa, in which he dealt particularly with "the ordinary life and pursuits, the habits and feelings of the natives" and the economic value of the countries traversed. In 1864 he was awarded the patron's medal of the Royal Geographical Society, and in 1866 given the Companionship of the Bath in recognition of his services in the expedition
Grant served in the intelligence department of the Abyssinian expedition of 1868; for this he was made C.S.I and received the Abyssinian medal. At the close of the war he retired from the army with the rank of lieutenant-colonel
Grant had married in 1865, and he now settled down at Nairn, where he died in 1892. He made contributions to the journals of various learned societies, the most notable being the "Botany of the Speke and Grant Expedition" in vol. xxix. of the Transactions of the Linnaean Society.
This text has been adapted from the 1911 Encyclopaedia Britannica.