A power steering system makes use of an electric motor to produce an auxiliary torque added to the torque which is applied to the steering wheel of a vehicle by the driver. The system includes a motor driver for driving the motor and a motor braking circuit for braking the motor. When the torque manually applied to the steering shaft of the vehicle is greater than a predetermined reference torque, an electronic control apparatus causes the motor driver to energize the motor according to the difference between these two torques. When the former torque is less than the reference torque, the control apparatus causes the motor braking circuit to brake the motor. In this way, the torque that the driver of the vehicle must apply to steer the vehicle is maintained equal to the reference torque, irrespective of the vehicle velocity. The reference torque is set by means of a variable-resistor.