An electric power steering control apparatus can reduce steering torque even in a steering holding state or a slight steering state without providing an unpleasant feeling to a driver. The apparatus includes a torque sensor for detecting steering torque generated by the driver for a vehicle, a motor for generating assist torque to assist the steering torque, a rotational speed detector for detecting the rotational speed of the motor, a torque controller for calculating an assist torque current corresponding to the assist torque based on the steering torque, and a damping control section for calculating a damping current to be added to the assist torque current to suppress vibrations generated in a steering system of the vehicle. The damping controller reduces a damping control gain to calculate the damping current when the rotational speed of the motor is equal to or less than a predetermined speed.
