An electric power steering apparatus 1 comprises an electric motor 8, a vehicle speed detecting section (vehicle speed sensor) VS, a shifting state detecting section for detecting a shifting state of the vehicle, an engine rotational speed detecting section (engine rotational speed sensor) ES, and a motor control section (controller) 12 for controlling drive of the electric motor 8. The motor control section 12 includes a failure determination section (vehicle speed sensor failure determination section) 21 for determining failure of the vehicle speed detecting section on the basis of a vehicle speed, a shifting state and an engine rotational speed. The failure determination section 21 determines that the vehicle speed detecting section VS malfunctions if the engine rotational speed is equal to or greater than a predetermined rotational speed for a determinative continuous-time and/or a first determinative integrated time while the vehicle speed is zero and the shifting state is a vehicle driving state.