In order to exploit the advantages of Tuned Tandem Mass Dampers‐Inerters（TTMDI），further improve its effectiveness and robustness，and enable it to be widely used in practical projects. The Nonlinear Fluid Viscous Damper-Tuned Tandem Mass Dampers ‐ Inerters（NFVD-TTMDI）system is presented. In the frequency domain，the semi-analytical solution of the dynamic amplification coefficient of the structure-NFVD-TTMDI system is derived，and the optimization criterion of the NFVD-TTMDI system is defined. Iterative method is used for equivalent linearization and FMINCON algorithm is used for optimization. The influences of different damping exponents v on the optimal parameters，the effectiveness of vibration reduction，the robustness and the mass block stroke of NFVD-TTMDI system are studied and verified in time domain. Numerical results show that，compared with linear TTMDI，NFVD-TTMDI not only has similar high control performance，but also significantly improves its robustness and reduces the demand for damping coefficient. These advantages make NFVD-TTMDI more economical and effective in practical engineering.