Based on inerter-spring-damper structural system, a passive realization method of ideal skyhook damping was presented by using the anti-resonance of the inerter-spring-mass system. A passive skyhook-damping suspension system was designed. The whole car model of the suspension was built to compare the performance of conventional passive, ideal skyhook-damping and passive skyhook-damping suspensions. The results showed that in contrast to conventional suspension, passive skyhook-damping suspension could suppress vertical, pitch and roll vibration of vehicle body with frequency of 1~3 Hz. The RMS values of vertical, pitch and roll acceleration reduced by 14%, 14.6% and 9.3%, respectively. The proposed suspension could improve ride comfort and achieve the main functions of ideal skyhook-damping suspension. The results also indicated that the passive realization method of ideal skyhook damping was corrective and effective. 