An electric power steering apparatus comprising: an operating member which is operated by a driver to steer a vehicle; a torque detector for detecting a torque generated by a steering system of the vehicle; a vehicle speed detector for detecting a vehicle speed of the vehicle; a motor for applying an assistive torque (Ta) to a rotational shaft of the steering system; a rotational angle detector for detecting a rotational angle of the steering system; and a motor controller for controlling an electric current for energizing the motor based on the torque detected by the torque detector, wherein the electric power steering apparatus also includes: an abnormality detector for detecting whether the torque detector becomes abnormal or not; and a storage unit storing, as a characteristic, a relationship between the rotational angle detected by the rotational angle detector and the electric current for energizing the motor; wherein when the abnormality detector detects an abnormality of the torque detector, the motor controller energizes the motor based on the rotational angle detected by the rotational angle detector and the characteristic, characterized in that when the motor is energized, the motor controller starts a process of reducing an electric current for energizing the motor if the absolute value (| θ sc'|) of a rotational angular velocity calculated based on the rotational angle is equal to or smaller than a prescribed value ( θ sc'tha), and interrupts the process of reducing the electric current for energizing the motor if the absolute value (| θ sc'|) of the rotational angular velocity continues to be equal to or smaller than the prescribed value for a prescribed time (Tkth). an operating member which is operated by a driver to steer a vehicle; a torque detector for detecting a torque generated by a steering system of the vehicle; a vehicle speed detector for detecting a vehicle speed of the vehicle; a motor for applying an assistive torque (Ta) to a rotational shaft of the steering system; a rotational angle detector for detecting a rotational angle of the steering system; and a motor controller for controlling an electric current for energizing the motor based on the torque detected by the torque detector, wherein the electric power steering apparatus also includes: an abnormality detector for detecting whether the torque detector becomes abnormal or not; and a storage unit storing, as a characteristic, a relationship between the rotational angle detected by the rotational angle detector and the electric current for energizing the motor; wherein when the abnormality detector detects an abnormality of the torque detector, the motor controller energizes the motor based on the rotational angle detected by the rotational angle detector and the characteristic, characterized in that when the motor is energized, the motor controller starts a process of reducing an electric current for energizing the motor if the absolute value (| θ sc'|) of a rotational angular velocity calculated based on the rotational angle is equal to or smaller than a prescribed value ( θ sc'tha), and interrupts the process of reducing the electric current for energizing the motor if the absolute value (| θ sc'|) of the rotational angular velocity continues to be equal to or smaller than the prescribed value for a prescribed time (Tkth). an abnormality detector for detecting whether the torque detector becomes abnormal or not; and a storage unit storing, as a characteristic, a relationship between the rotational angle detected by the rotational angle detector and the electric current for energizing the motor; wherein when the abnormality detector detects an abnormality of the torque detector, the motor controller energizes the motor based on the rotational angle detected by the rotational angle detector and the characteristic, characterized in that when the motor is energized, the motor controller starts a process of reducing an electric current for energizing the motor if the absolute value (| θ sc'|) of a rotational angular velocity calculated based on the rotational angle is equal to or smaller than a prescribed value ( θ sc'tha), and interrupts the process of reducing the electric current for energizing the motor if the absolute value (| θ sc'|) of the rotational angular velocity continues to be equal to or smaller than the prescribed value for a prescribed time (Tkth).