A steering system for a vehicle having a steering wheel and front and rear wheels, including a front steering sub-system for steering the front wheels in accordance with the steering angle of the steering wheel and a rear steering sub-system for steering the rear wheels in the same and opposite directions with respect to the front wheels in accordance with the steering angle of the steering wheel. The steering system is provided with a rack and pinion type variable-ratio mechanism for varying the ratio of the steered angle of at least either of the front or rear wheels to the steering angle of the steering wheel in accordance with the magnitude of the steering angle of the steering wheel. The design freedom in setting a functional relation between the steering angle of the steering wheel and the turning curvature of the vehicle is thus maximized. Moreover, selective setting is permitted for change of ratio of the steered angle of the rear wheels to the steering angle in the vicinity of the initial position of the steering wheel. Further, there is permitted a favorable use of available vehicle dimensions to achieve an optimum feeling characteristic of steering operation.