A front and rear wheel steering system for a vehicle which transmits a steering input from a front wheel steering gear box to a rear wheel steering gear box via a coupling shaft as a rotation thereof around its longitudinal line and varies a steering gear ratio of rear wheels to front wheels according to the speed of the vehicle. A steering rod for steering the rear wheels with its longitudinal movement is provided with a crank portion which is engaged with a swing shaft pivotally attached to the coupling shaft via a pivot shaft perpendicular thereto so as to perform a gyrating motion around an extension line of the coupling shaft and thereby move the steering rod along its longitudinal direction to achieve a steering action of the rear wheels. The steering rod can be rotated around its longitudinal line according to the vehicle speed so as to displace the crank portion relative to the extension line of the coupling shaft and change the relationship between the rotational angle of the coupling shaft or the steering input to the front wheel steering gear box and the longitudinal movement of the steering rod or the steering angle of the rear wheels.