An apparatus for steering a vehicle includes a hand steering device, a road wheel steering device, a steering motor and a connection device. The hand steering device is a device which a driver of the vehicle manipulates for steering road wheels. The road wheel steering device actuates the road wheels. The steering motor, which is attached to the road wheel steering device, produces an assist force for the road wheels. The connection device selectively connects and disconnects the hand steering device and the road wheel steering device. In the apparatus, a ratio of a displacement made by the hand steering device to a displacement generated by the road wheel steering device increases as a speed of the vehicle becomes greater while the vehicle is traveling in a predetermined range of speed, and a gradient of the ratio is adapted to be greater when the speed is lower.