Conrad Baker (February 12, 1817 – April 28, 1885) was a state representative, 15th Lieutenant Governor, and the 15th Governor of the U.S. state of Indiana from 1867 to 1873. Baker had served in the Union Army during the American Civil War, rising to the rank of colonel but resigned following his election as lieutenant governor, during which time he played an important role in overseeing the formation and training of states levies.