Abstract—In generally, a suspension system needs to be soft to insulate against road disturbances and hard to insulate against load disturbances. It cannot achieve with a traditional passive suspension that only considered to the stiffness and damper. In this study, the paper clarifies some issues related to suspension system with inerter to reduce sprung mass displacement and tire deflection in quarter-car model. In this paper, we integrate some kinds of suspension system with inerter on quarter-car models. We propose some new designs, which have some advantages for suspension system by improving vehicle oscillation. We optimize design of model based on the minimization of cost functions for displacement, tie deflection with constraint function of suspension deflection limitation and the energy consumed by the inerter. The advantage of research is integration a new mechanism, the inerter; this system can improve the vehicle oscillation on quarter-car model with different parameters. It shows the benefit of the inerter in proposal suspension system.