As a new type of vibration reduction, the ladder track system has been successfully used in engineering. In this paper, a numerical model of the train-track-viaduct system is established to study the dynamic responses of an elevated bridge with ladder track. The system is composed of a vehicle submodel, a track submodel and a bridge submodel, with the measured track irregularities as the system self-excitation. The whole time histories of a train running through an elevated bridge with $3{ imes}27m$ continuous PC box girders are simulated. The dynamic responses of the bridge such as deflections, lateral and vertical accelerations, and the vehicle responses such as derailment factors, offload factors and car-body accelerations are calculated. The calculated results are partly validated through the comparison with the experimental data. Compared to the common slab track, adapting the ladder sleeper can effectively reduce the accelerations of the bridge girder, and also reduce the car-body accelerations and offload factors of the train vehicle.