Abstract: In order to control the train-induced low-frequency ambient vibration, we apply the tuned inerter damper (TID) to the steel-spring floating slab track (FST) and propose a novel TID-vibration-isolator FST structure in this study. The low-frequency elastic wave propagation properties of the TID-vibration-isolator FST structure and its vibration characteristics under the harmonic point load are elucidated. Moreover, the TID parameter is optimized with the multi-objective genetic algorithm. Then, the low-frequency vibration-mitigation characteristics of the TID-vibration-isolator FST under train loads are investigated based on the vertical coupled dynamics model of a vehicle-TID vibration isolator FST-foundation system. The results show that a new band gap of the bending wave occurs in the TID-vibration-isolator FST. Due to the inhibition of the bending wave propagation arising from the band gap, the receptance amplitude peak of the foundation at the low resonance frequency of the floating slab disappear. The low-frequency vibration-mitigation performance in the frequency range of 4 Hz~16 Hz is improved in this novel track structure. Besides, vibration responses of the floating slab are attenuated.