Minor noble, civil servant and father of mathematician John Napier (1550 - 1617). Born in Merchiston (Edinburgh), where the family had land since the 1430s and had built a castle. The family also owned estates at Lennox and at Menteith, together with a home at Gartness.
Napier became the 7th Laird of Merchiston having married Janet Bothwell, the sister of the Bishop of Orkney, when he was only 15 years old (1549). Their son John was born the following year. Janet died at Merchiston in 1564. The Napier family had come to prominence, and gained their wealth, through service of successive Kings and Archibald continued this tradition. He served as a Justice-Depute, was knighted in 1565 and appointed Master of the Mint in 1582.
Napier died at Merchiston.