The preview control problem of vehicle suspension is discussed. The optimal transfer function of a preview filter is determined under a criterion function which is constructed by the weighted sum of the mean squared value of the vertical acceleration on an arbitrary point of a two-dimensional rigid vehicle body and the relative displacement of rear suspension. In some numerical examples, the rms value of vertical acceleration of the center of gravity of the body is reduced to about one seventh that of a system with passive elements only and to about two fifths that of an optimally controlled system without future value of input under the same constraints on relative displacement of rear suspension. It is possible to design this system to be safe side, even under conditions it was not designed for.