Based on vibration state in transition from the mass to the inerter, a passive realization method of ideal skyhook damping was presented. According to such a method, a passive groundhook-damping suspension was designed. After the simscape model of the inerter was founded, the full-car simscape model was built by using the network approach of physical topology. By comparing the performances of conventional passive, ideal and passive groundhook-damping suspensions, the proposed realization method was verified. The results show that the proposed suspension can suppress wheel resonance, reduce RMS values of dynamic tire load by 30% or greater, and significantly improves ride safety. The results also indicate the performances of the ideal and passive groundhook-damping suspensions are basically the same.