The power steering apparatus comprises a torque sensor for detecting a steering torque applied to a steering wheel and a steering assist motor which is driven to rotate based on the detected steering torque. The motor is driven under field weakening control in a high-speed rotation area. The motor is a brushless motor comprising a rotor having a plurality of permanent magnets which are respectively fixed in a plurality of recesses provided in a rotor core. With the electric power steering apparatus, a steer-assisting force can be obtained in high-speed steering.