Son and nephew of famous inventors, Maxim graduated from Massachusetts Institute of Technology, then in Boston, at age 16 and by 1890 was superintendent of the American Projectile Company plant at Lynn, Mass. While bicycling from Salem to Lynn, he conceived the idea for a gasoline-powered tricycle, which he built by 1895, leading to his employment by the Pope Manufacturing Company of Hartford, Conn. There he supervised production of the vehicle and also designed an electric automobile, the Columbia, which the company manufactured for several years.

His efforts to improve the gasoline-powered automobile led to research on the exhaust muffler, which in turn brought the discovery of the principle that made possible the famous “silencer.” This invention brought him fame, and even notoriety, as editors, writers, and the general public mistakenly assumed that the device could be attached to the pistols of criminals; in actuality, it was usable only on a sealed-breech rifle and never found wide demand. The ensuing furor led to its prohibition in many states in the United States and in several other countries and caused Maxim to stop its manufacture in 1930. He adapted the principle to mufflers, safety valves, air compressors and blowers, and other devices.

In his later years Maxim became a champion of the rights of amateur radio operators and was instrumental in opening shortwave and ultra-shortwave radio to them.