Technology for reducing track vibrations is a key approach to limiting the propagation of vibrations during train operation, yet existing damping tracks still have room for improvement. Derived from the existing sleeper-damping track (ESDT) and the sleeper-damping track with elastic side-supporting pads (SDTESSP) structures, a new sleeper-damping track with elastic composite-supporting pads (SDTECSP) was developed in this paper. To evaluate the dynamic performance of SDTECSP, finite element models (FEMs) and dynamic models were established for different damping tracks. First, under the same load and support stiffness, the stress distribution characteristics of floating-slab track (FST), ESDT, SDTESSP, and SDTECSP were compared and analyzed. And the stress concentration areas of the rail, sleeper, and track bed were identified. Then, the accuracy of the SDTECSP model was verified by the impact test of drop hammer. Finally, the dynamic performance of the track subsystem and the vehicle subsystem for four damping tracks was effectively evaluated by the combination of field test and simulation. The influence of different vehicle speeds on the track subsystem was analyzed. The results show that compared to FST, ESDT, SDTESSP, and SDTECSP exhibit superior performance in vibration damping capability, structural stability, and structural optimization design.