Follow-up steering control is executed in a vehicle speed region where vehicle speed V0 is less than V1, and for a vehicle speed region to the higher speed side, a target yaw rate .gamma.t for the vehicle is calculated depending on the current positions of a preceding vehicle and the vehicle, and a power steering instructed current value ic for following up the preceding vehicle is calculated based on the target yaw rate .gamma.t and output to an electrical power steering control unit. On the other hand, for a vehicle speed region to the lower speed side, a target steering angle St for the vehicle is calculated depending on the current positions of the preceding vehicle and the vehicle, and a power steering instructed current value ic for following up the preceding vehicle is calculated based on the target steering angle St.