Grant was the fourth son of Francis Grant, Laird of Kilgraston, near Bridge of Earn, Perthshire, and his wife Anne Oliphant of Rossie. Grant was educated at Harrow School and Edinburgh High School. His father, a plantation owner in Jamaica, died in 1818, leaving money to his seven children. Initially Grant intended to become a lawyer, but he left his studies after a year, and took up painting. He possibly spent time in the Edinburgh studio of Alexander Nasmyth. Grant through his second wife gained access to a clientele in the hunting set at Melton Mowbray, where he hunted himself, and took lessons with the artist John Ferneley. He acquired a reputation as a painter of sporting subjects, and in 1834 exhibited at the Royal Academy a picture called Melton Breakfast which was engraved by Charles George Lewis. In 1840 he exhibited an equestrian group of Queen Victoria riding with Lord Melbourne and others in Windsor Park, and became the fashionable portrait-painter of the day. His portrait of Lady Glenlyon, exhibited in 1842, increased his reputation, and for nearly 40 years graceful portraits in the Royal Academy exhibitions came from his studio. Elected an associate of the Royal Academy in 1842, Grant in 1851 became an academician. In 1866, on the death of Charles Eastlake, Edwin Landseer turned down the seat of Academy President, and Grant was elected instead. He was knighted that year.
After some years of gradually failing health, Grant died of heart disease suddenly at his residence, The Lodge, Melton Mowbray, on 5 October 1878, and was interred in the Anglican cemetery, his relations having declined the usual honour of burial in St Paul's Cathedral. His funeral was conducted by the Archbishop of York on 12 October and many of the leading British artists attended, including Edward John Poynter, Edward Armitage, Thomas Woolner, Philip Hermogenes Calderon, and the American Albert Bierstadt.
Family
Grant married, firstly, Amelia Farquharson, the daughter of a Scottish laird, in 1826; she died after giving birth to their son. He married again, in 1829, Isabella Elizabeth Norman, daughter of Richard Norman and his wife Lady Elizabeth Isabella, and a niece of John Manners, 5th Duke of Rutland; they had three sons and four daughters. Among the sons was Ferdinand Hope-Grant, a chaplain to the Prince of Wales. One of the daughters was Anne Emily Sophia Grant, whose portrait, by her father, hangs in the National Gallery of Scotland, and has been noted for its depiction of Victorian womanhood. Grant was the brother of General Sir James Hope Grant. Mary Grant, the eminent Victorian sculptress, was his niece.