The vibration responses of a 3D random model for a vehicle-bridge system subjected to running vehicle at nonconstant speed are resolved by pseudo excitation method (PEM) based on a consistent stimulus of road roughness. Taking multipoint coherent road roughness excitation into condition, a new 3D random vibration model for vehicle-bridge systems is proposed. In the vehicle-bridge coupling model, the bridge is,modeled as a beam-shell solid element, the vehicle is simplified as a 3D freedom model with nine degrees and the load caused by the road roughness is equivalent to a pseudo excitation load. The model is resolved by a precise integration method (PIM), and the accuracy of results is verified through comparing with the results of a Monte-Carlo method. Taking one highway beam bridge as an example, different point dynamic responses of the bridge subjected to uniformly accelerating vehicle have been researched. The results prove the accuracy and feasibility of the vehicle-bridge coupling random vibration model which has been proposed in the paper. The vehicle speed is the most fact which leads to a peak displacement and a peak acceleration at mid-span with the same road roughness excitation. There is more large resonance frequency region when the vehicle runs on bridge with a nonconstant speed than a constant one. The peak displacement and peak acceleration at mid-span of growth appears fast followed by slow when the vehicle speed increases gradually.