[1] Napier entered the Royal Naval Academy at Portsmouth Dockyard on 5 May 1803, and on 20 September 1806 joined the 74-gun Spencer, as a first-class volunteer.

In her under the Captains the Honourable Robert Stopford and John Quilliam, he visited the Cape of Good Hope, and as a midshipman took part in the Bombardment of Copenhagen, also assisting in the destruction of Fleckeroe Castle, on the coast of Norway.

On 7 June 1814, he was promoted to commander aboard the 18-gun sloop Goree at Bermuda; and soon after appointed to the brig-sloop Rifleman, employed in protecting merchant vessels in the Bay of Fundy.

In August 1815 Napier went on half-pay, having declined accepting a piece of plate that had been voted to him for his care in the conduct of convoys between the port of Saint John, New Brunswick and Castine, Maine.

His chief work was the Florentine History from the earliest Authentic Records to the Accession of Ferdinand the Third, Grandduke of Tuscany, in six volumes, published in 1846–47.