In a front and rear wheel steering device for a vehicle in which the steering angle ratio of the rear wheels relative to the front wheels is variable according to the vehicle speed, by accounting for the magnitude of vehicle acceleration in determining the steering angle ratio of the rear wheels by selecting a mathematical function from a plurality thereof, the vehicle response particularly in high speed range can be improved. Smooth transition from a certain characteristics to another may be achieved either by preparing a number of mathematical functions of vehicle speed for the steering angle ratio of the rear wheels or providing some time delay in the transition from one characteristics to another, preferably in proportion to the magnitude of the vehicle acceleration.