An electric steering system includes a steering torque measuring device for measuring a steering torque input into a steering system, a steering speed measuring device for measuring a steering speed of the steering system; a target current computing section for computing a target current based on the steering torque measured by the steering torque measuring device, and a control section for applying a steering power to the steering system by driving a motor according to the target current. When the measured steering speed is less than a predetermined speed value, the control section applies damping to the steering system based on the measured steering speed and when it is not the control section performs a control operation of adding a specified steering torque defined when the steering speed is equal to the predetermined speed value and an increment for the steering torque determined in accordance with the steering speed to each other, defining the sum of the addition as a target steering torque, and controlling the target current so that the measured steering torque coincides with the target steering torque.