The present invention provides an excellent electric power steering apparatus in which torque ripple caused by a quantization error of a current control system generated in case of slow steering state and steering holding state, namely, vibration and noise on a steering wheel can be suppressed. A current controller in which a steady state gain of feedback control is a finite value is used so as to be capable of suppressing the vibration and noise. Further, according to the present invention, a smoothing filter is included in a current control system so that the quantization error is smoothed so that the torque ripple is suppressed.