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 converts into an anticipated lateral acceleration Gd based upon the steering torque Td. A turning angle conversion section 55 calculates target turning angles .delta.d. A turning angle correcting section 61 obtains a slip angle .beta. of a slip generated on a vehicle. Then, the turning angle correcting section 61 corrects the target turning angle .delta.d based upon the obtained slip angle .beta., thereby calculating a corrected target turning angle .delta.da. A drive control section 63 controls the steered wheels to be turned into the corrected target turning angle .delta.da. According to this, a driver can correctly perceive the generated anticipated lateral acceleration Gd, whereby he/she can easily drive the vehicle.