In a vehicle steering apparatus of a steer-by-wire system, front wheels are controlled to be turned by a computer program processing. A displacement/torque conversion section 51 converts a steering angle .theta. into a steering torque Td that is in relation of exponential function. A torque/lateral-acceleration conversion section 52 converts the steering torque Td into an anticipated lateral acceleration Gd (or anticipated yaw rate .gamma.d and anticipated turning curvature .rho.d) that is in relation of exponentiation function and that serves as a vehicle motion state quantity that can be perceived by a human. A turning angle conversion section 53 calculates a target turning angles .delta.d necessary for the vehicle to move with the anticipated lateral acceleration Gd (or anticipated yaw rate .gamma.d and anticipated turning curvature .rho.d). A turning control section 60 controls the steered wheels to be turned into the target turning angle .delta.d. A driver turns the handle, feeling the lateral acceleration, and hence, the driver can easily drive the vehicle.