In this paper the approximate dynamic model of an active car body suspension system is presented on the basis of which a fractional order active controller is designed to reduce jogging of the payload carried by the car. Besides the conventional springs of viscous damping the model includes an air spring, and a dashpot with hydraulic nonlinearities. Dissipative phenomena in the air spring are also modeled. The role of the fractional order controller is to introduce frequency-dependent damping of the forced oscillation of the system caused hills and valleys as well as by small dips and bumps on the road. It is pointed out that while the dashpot system serves as a nonlinear component saving the floor of the chassis its frequency transmission properties are undesirable in the higher frequency part of the excitation. The fractional order controller can compensate this undesirable effect. Simulation results are presented to demonstrate the operation of the proposed control.