James Glenie was educated at St Andrews, where he was briefly an assistant in mathematics. Glenie then qualified as an engineer at the Royal Military Academy, Woolwich. He was an artillery officer in the American War of Independence and taught (1805-10) at the East India Company Royal Military College at Addiscombe.
Glenie served as a member of the New Brunswick House of Assembly and failed in a business venture, dying in poverty.
He wrote several journal articles, also books on Gunnery (1776) and Antecedental Calculus (1793, 1794), an attempt to base fluxional calculus on the binomial theorem rather than on the concept of motion.