Born in Edinburgh, Napier studied at the University of St. Andrews but left before taking his degree and then traveled extensively throughout Europe. He was a fervent Protestant and wrote a diatribe attacking Catholics and others whose religious views he disapproved of. Napier was also very active in politics and he designed a number of war-engines of various kinds when it was believed that the Spanish were about to invade Scotland.

Napier devoted his spare time to mathematics, in particular to methods of computation. He introduced the concept of logarithms, publishing his work on this in Mirifici logarithmorum canonis descriptio (1614; Description of the Marvelous Canon of Logarithms). Napier's tables used natural logarithms, i.e., to base e, and soon after their publication the tables were slightly modified by Henry Briggs to base 10. Napier's further work on logarithms was published after his death in Mirifici logarithmorum canonis constructio (1619; Construction of the Marvelous Canon of Logarithms). Napier did some other mathematical work, in particular in spherical trigonometry and in perfecting the decimal notation.