A variable-ratio steering system includes a steering shaft connected to a manually-operated handle, a ball nut engaging with the steering shaft and a ball-bearing-screw mechanism converting rotary motion of the steering shaft into axial displacement of the ball nut in the axial direction of the steering shaft. Also provided is a second motion converter which generates a rotational displacement of the ball nut about the axis of the steering shaft with the axial displacement of the ball nut. A steering pinion gear block is connected to the ball nut by means of serrations to rotate together with the ball nut. A rack is engaged with the pinion gear block and connected at both ends via knuckle mechanisms to steered wheels for varying a steer angle at the steered wheels depending on the displacement of the rack. The second motion converter having a variable steering ratio mechanism which varies a ratio of a rotational displacement of the ball nut about the axis of the steering shaft to the axial displacement of the ball nut to vary a steering ratio of steering wheel rotation angle to road-wheel steer angle.