A device for controlling damping coefficients of shock absorbers (22FL, 22FR, 22RL, 22RR) of a four wheeled vehicle constructs a phantom damping system composed of a phantom side shock absorber (122, 122F, 122R) disposed vertically at a lateral inside of a turn running of the vehicle to have a lower end movable along a ground surface together with the vehicle and an upper end vertically movable relative to the lower end with a first phantom damping coefficient (Cg, Cgf, Cgr) therebetween, and a phantom angular shock absorber (124, 124F, 124R) arranged to act between the upper end of the phantom side shock absorber and the vehicle body with a second phantom damping coefficient (Ca, Caf, Car) therebetween, whereby, when the damping coefficients of the shock absorbers are controlled to substantially equalize the phantom damping system with the actual damping system of the actual shock absorbers with respect to damping vertical and rolling movements of the vehicle body, the mass center of the vehicle body is lowered according to a rolling thereof during a turn running of the vehicle, as the vehicle body rolls around the upper end of the phantom side shock absorber located laterally inside of the turn running.