In order to improve the effective working frequency band and overcome the practical limitations caused by the large tuning mass required, the inertial double tuned mass nonlinear energy sink(IDTM-NES) is proposed by combining an inerter with a nonlinear energy sink, and its seismic reduction performance is studied. A single-degree-of-freedom system with IDTM-NES is established, and its construction parameters are numerically optimized using the Runge-Kutta algorithm. The different seismic excitation responses and the damping energy dissipation curve over time are compared with TMD and NES. In addition, the time-frequency distribution of vibration response energy is studied through wavelet transform. The research results indicate that the IDTM-NES can better improve the damping energy dissipation performance and effectively reduce the seismic response of the controlled main structure and tuned substructure, and also has better robustness considering the stiffness changes of the main structure. Furthermore, the results demonstrate the rich instantaneous resonance capture behavior is generated by the IDTM-NES in a wider frequency domain, which reveals the damping mechanism of IDTM-NES.