An electric power steering apparatus compensates a dead time of an inverter without tuning operation, improves distortion of a current waveform and responsibility of a current control, and suppresses sound, vibration and ripple. The apparatus calculates dq-axes steering-assist command values based on at least a steering torque, calculates dq-axes current command values from the dq-axes steering-assist command values, converts the dq-axes current command values into 3-phase duty command values, driving-controls a 3-phase brushless motor by an inverter of a PWM control, and applies an assist torque to a steering system of a vehicle. Dead time reference compensation values are calculated based on a motor rotational angle. Dead time compensation of the inverter adds dead time compensation values in which the dead time reference compensation values are processed by using a gain, a sign and the like, to dq-axes voltage command values or to 3-phase voltage command values.