Base-isolation method performs well in controlling superstructure responses but is limited in maintaining stability with special earthquake like long-period earthquakes or extreme rare earthquakes. This study proposes an inerter-based hybrid isolation system which can improve the robustness of isolation structure, utilizing traditional linear natural rubber bearing (LNR), elastic slide bearing (ESB) and viscous damper combined with acceleration-dependent inerter. A two-stage optimal design method is also proposed by leveraging the synergistic effect of the inerter and stiffness of isolation layer. The proposed system can effectively reduce the crucial responses and increase the robustness of isolation structure. This paper firstly builds the inerter-based hybrid isolation structure. Then, the key parameters are classified into two parts based on period-correlation. And the two-stage optimal method is introduced utilizing parameters. An actual engineering structure is used to investigate the feasibility of the inerter-based hybrid isolation system and the optimal method under rare and extreme rare earthquakes. A U-shape high-strength-and-toughness-steel (HSTS) is employed to bear part of stiffness in the isolation layer which brings negative and nonlinear stiffness. Further, displacement and acceleration depended indicators is introduced to evaluate the robustness of structure. The results show that by employing the inerter, the displacement and acceleration responses both decrease compare to the traditional isolation structure without inerter while keeps the isolation layer displacement in the same level. The inerter-based hybrid isolation system can also increase the robustness under extreme rare earthquake. It provides a new reference for combining different types of mechanics components to improve the performance of isolation method, enhancing the safety, stability, and comfort of structures.