A steer-by-wire steering system, comprising: a hydraulic actuator for changing a turning angle of an object to be steered; a pump for supplying hydraulic pressure to the hydraulic actuator; an electric motor for rotating the pump in forward and reverse directions to operate the hydraulic actuator; a steering angle sensor for detecting a steering angle of a steering; a turning angle sensor for detecting the turning angle; and a control device for operating the electric motor according to signals from the steering angle sensor and the turning angle sensor to control the turning angle to be corresponded to the steering angle, wherein: the control device comprises: a steering angle receiving unit for receiving a signal from the steering angle sensor; a turning angle receiving unit for receiving a signal from the turning angle sensor; a deviation determining unit for sequentially determining a deviation between the steering angle and the turning angle according to the signals received by the steering angle receiving unit and the turning angle receiving unit; a motor driving unit for outputting a control signal to the electric motor in a direction of decreasing the deviation determined by the deviation determining unit to control the electric motor characterized in that the system further comprises a control correction unit for changing the control signal in a direction of decreasing a time lag according to the time lag between a change in the steering angle and a change in the turning angle derived according to the deviation, wherein in a case a lag between the steering angle and the turning angle is lower than a first threshold, the control correction unit controls rotation speeds of the electric motor and pump by referring to a first target voltage map; in case a lag between the steering angle and the turning angle becomes larger than a first threshold, the control correction unit determines that volumetric efficiency of the pump decreases and raises rotation speeds of the electric motor and pump by referring to a second target voltage map; and in a case a lag between the steering angle and the turning angle becomes lower than a first threshold, the control correction unit determines that volumetric efficiency of the pump is recovered, and reduces rotation speeds of the electric motor and pump by referring to the first target voltage map, so as to compensate for reduction of the volumetric efficiency, wherein a duty ratio of a PWM pulse signal output to the electric motor determined by referring to the second target voltage map is greater than the duty ratio determined by referring to the first target voltage with respect to a same target turning angle. the control device comprises: a steering angle receiving unit for receiving a signal from the steering angle sensor; a turning angle receiving unit for receiving a signal from the turning angle sensor; a deviation determining unit for sequentially determining a deviation between the steering angle and the turning angle according to the signals received by the steering angle receiving unit and the turning angle receiving unit; a motor driving unit for outputting a control signal to the electric motor in a direction of decreasing the deviation determined by the deviation determining unit to control the electric motor characterized in that the system further comprises a control correction unit for changing the control signal in a direction of decreasing a time lag according to the time lag between a change in the steering angle and a change in the turning angle derived according to the deviation, wherein in a case a lag between the steering angle and the turning angle is lower than a first threshold, the control correction unit controls rotation speeds of the electric motor and pump by referring to a first target voltage map; in case a lag between the steering angle and the turning angle becomes larger than a first threshold, the control correction unit determines that volumetric efficiency of the pump decreases and raises rotation speeds of the electric motor and pump by referring to a second target voltage map; and in a case a lag between the steering angle and the turning angle becomes lower than a first threshold, the control correction unit determines that volumetric efficiency of the pump is recovered, and reduces rotation speeds of the electric motor and pump by referring to the first target voltage map, so as to compensate for reduction of the volumetric efficiency, wherein a duty ratio of a PWM pulse signal output to the electric motor determined by referring to the second target voltage map is greater than the duty ratio determined by referring to the first target voltage with respect to a same target turning angle.