An $Hinfty$ controller is designed for active suspensions of vehicles using 7-degree-of-freedom full-car model. Its performance robustness as well as stability robustness to system parameter variations and unmodelled dynamics are assured through the $mu$-framework. The performance of the $Hinfty$ controller is compared with that of a LQC controller in compute simulations. From the simulations it is found that the active suspension with the $Hinfty$ controller reduces the acceleration and motion of the sprung mass in the heaving rolling and pitching directions when the car is driven on a normal road or through an asymmetric bump. The suspension stroke and the road holding capability are also improved with a relatively small level of power consumption. Overall the $Hinfty$ controller shows a more robust performance than that of the LQG design.