An electric power steering system for a vehicle works to determine an assist command based on steering torque to produce assist torque through an electric motor for assisting in turning a steering wheel of the vehicle, also determines a tracking command for producing automatic steering torque which brings a value of a given physical quantity associated with steering of the vehicle into agreement a target value, and calculates a vibration correction command for use in producing vibration correction torque which suppresses vibration of the steering torque which arises from output of the torque from the electric motor based on a transfer characteristic of transmission of the output of torque from the electric motor as a part of the steering torque through the steering mechanism. A motor driver works to actuate the electric motor based on the sum of the assist command, the tracking command, and the vibration correction command.