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 （TTMDI）. The Bouc-Wen hysteretic model is used to simulate the nonlinear force-deformation behaviors of the isolation layer. Employing the stochastic equivalent linearization，pattern search optimization algorithm，as well as the earthquake ground motion model simultaneously，the optimum design framework of the BIS+TTMDI system is established in the frequency domain. The performance of the BIS+TTMDI system is systematically evaluated in terms of its robustness，effectiveness，stiffness and damping coefficient，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.