The ladder-type sleeper track (LS track) is one of the traditional vibration-attenuating track systems. Based on engineering experience, a vibration suppression device (VSD) for the LS track has been developed to reduce LS track vibration caused by metro trains and improve train running stability. In this work, numerical simulation was used to investigate the effect of essential VSD parameters such as stiffness, damping, and preload on the dynamic responses of the vehicle-LS track system. Firstly, a refined vehicle-LS track coupled dynamics model involving an elaborated model of VSD was developed to investigate the action principle of VSD and the influence of various action methods on LS track vibration suppression. Then, the effects of VSD were thoroughly investigated using the proposed model from the perspectives of vehicle-track dynamic interaction, vehicle dynamics, and LS track’s stability and vibration attenuation capabilities. Finally, the influence tendency of major VSD parameters on vehicle and LS track dynamic performance, as well as the range of VSD parameters engineering feasibility, was explored. The results show that VSD features can affect the vehicle-LS track dynamics performance. VSD not only reduces LS track vibration, but also improves vehicle’s operating stability, and VSD’s influence becomes more substantial with the rise of crucial VSD parameter values.