In a vehicle steering apparatus, 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, torque/yaw-rate conversion section 53 and torque/curvature conversion section 54 convert into an anticipated lateral acceleration Gd, anticipated yaw rate .gamma.d and anticipated turning curvature .rho.d based upon the steering torque Td. Turning angle conversion sections 55, 56 and 57 calculate target turning angles .delta.g, .delta..gamma. and .delta..rho.. A turning angle deciding section 58 decides a target turning angle .delta.d among the target turning angles .delta.g, .delta..gamma. and .delta..rho. according to the detected vehicle speed V. A turning control section 60 controls the steered wheels to be turned into the target turning angle .delta.d. Herewith, the vehicle steering apparatus of the present invention can turn the vehicle so as to be adapted to a man's perception characteristic in all speed areas with respect to an operation on a steering handle by a driver. Therefore, the driver can easily drive the vehicle in all speed areas.