In order to cope with excessive displacement requirements of the isolation layer in the base isolated structure， a hybrid isolation system is proposed in this paper through the base isolated system （BIS） + tuned tandem mass dampers-inerters （TTM? DI）. The Bouc-Wen hysteretic model is used to simulate the nonlinear force-deformation behaviors of the isolation layer. Employ? ing the stochastic equivalent linearization， pattern search optimization algorithm， as well as the earthquake ground motion model si? multaneously， the optimum design framework of the BIS+TTMDI system is established in the frequency domain. The perfor? mance of the BIS+TTMDI system is systematically evaluated in terms of its robustness， effectiveness， stiffness and damping co? efficient， stroke and sensitivity to seismic frequency contents， and compared with BIS + the tuned mass damper （TMD）， tandem tuned mass damper （TTMD）， and tuned mass damper-inerter （TMDI）， respectively. The dynamic elasto-plastic analysis of a seven story hybrid base-isolated system， respectively including the BIS+TTMDI and BIS+TMDI systems， is carried out under the near-field earthquake ground motions. The results show that the BIS+TTMDI system has the best seismic performance and strong robustness. Furthermore， the total damping requirement of the TTMDI in the BIS+TTMDI system is less than half of the TMDI in the BIS+TMDI system， which is more economical and practical.