Born in Charlotte County, Virginia, Speed was taught by his father Thomas Spencer Speed. He moved with his parents to Kentucky in 1782. He was employed in the office of the clerk of the general court. He engaged in mercantile pursuits at Danville and Bardstown in 1790. He also engaged in agricultural pursuits. He served as clerk of the Bullitt and Nelson circuit courts. He served as major of Volunteers in the War of 1812.
Speed was elected as a Democratic-Republican to the Fifteenth Congress (March 4, 1817 – March 3, 1819). He was an unsuccessful candidate for reelection. He resumed agricultural pursuits. He also contributed articles to the National Intelligencer, Washington, D.C.. He served as member of the State house of representatives in 1821, 1822, and again in 1840. He was a member of the Whig Party when it was organized. He died on his farm, near Bardstown, Kentucky, February 20, 1842. He was interred in Bardstown City Cemetery in Bardstown, Kentucky. Speed was one of Lincoln's best friends. He was married twice. With his first wife Sarah Whitney Sparhawk, he had two children: William O. Speed and Thomas Speed.