An electric power steering apparatus includes a steering assist torque control system in which a steering torque signal is input and a motor speed signal is output. The control system includes a main control value setting section having a gain KTT and setting a target assist torque value corresponding to the steering torque, a differential-value correction value setting section having a gain KTD and setting a differential-value correction value corresponding to a differential steering torque value, a motor having an inertial efficiency JM and a counter electromotive force (induced voltage) constant KE, a motor drive section incorporated in a controlled object and having a proportional gain KP, a steering speed correction value setting section having a gain KTR and setting a steering speed correction value corresponding to the motor speed signal. The ratio of the gain KTD to the gain KTT is set to satisfy the condition: KTD/KTT>JM/{.alpha.(KP.multidot.KTR+KE)} where .alpha.=KT/(R+KP), R is the resistance (winding resistance) of the electric motor, and KT is the torque constant of the electric motor. With this arrangement, the phase of a gain of the steering assist torque control system is advanced, thereby improving the response characteristic to a level at least comparable to the manual steering mechanism.