With the continuous increase of subway operating mileage, the problem of subway vibration has become more and more significant. Nowadays, the point-supported floating-slab track is recognized as the best method to control track vibration, which is mainly designed based on the mass-spring-damping theory. How to further improve the vibration control ability of the point-supported floating-slab track? In this paper, a new type of rubber point-supported floating slab track is designed based on the local resonance theory. Through calculation and dynamic test, it is obtained as follows: (1) The band gap of the point support structure by local resonance type depends on the two vertical vibration modes. (2) As the elastic modulus of the cladding layer increases, the bandwidth of the band gap of the corresponding structure increases significantly. (3) The increase of the vibrator density can increase the bandwidth, while reducing the start and stop frequencies, which is beneficial to attenuate the resonance of the floating-slab track. (4) The cushion material parameters of point support structure by local resonance type 2 will not affect the band gap. The increase in sleeve density will reduce the band gap, which is not conducive to vibration reduction. Local resonance type floating-slab track will be the development direction of track vibration-reduction measures in the future.