Abstract: This article investigates the optimization problem of a novel base isolation system by introducing a passive network consisting of one damper， one spring and one inerter and a grounded element with negative stiffness. The dynamic equations of the system are established and the frequency response function in the dimensionless form is derived. Since it is found that the amplitudefrequency response curves pass through four fixed-points， the extended fixed-point method is utilized to solve the parameter optimization problem. The explicit expressions of the optimal inertance-to-mass ratio， the optimal natural frequency ratio， and the optimal corner frequency ratio of the system are derived by adjusting the four fixed points to the same height. The expression of the optimal damping ratio is calculated by letting the amplitudes of the three invariant frequencies among the four fixed points to the same amplitudes as those of the four fixed-points. A necessary and sufficient condition for the system with optimal parameter values to be stable is derived by utilizing the Hurwitz stability criterion. Compared with other three optimal isolation systems， the optimal isolation system in this article can provide better H∞ performance and better output responses in the multi-storey building vibration system.