A new dynamic model of railway vehicle moving on curved tracks is proposed. In this new model, the motion of the car body is considered and the motion of the tuck frame is not restricted by a virtual boundary. Based on the heuristic nonlinear creep model, the nonlinear coupled differential equations of the motion of a fourteen degrees of freedom car system, considering the lateral displacement and the yaw angle of the each wheelset, the truck frame and the car body, moving on curved tracks are derived in completeness. To illustrate the accuracy of the analysis, the limiting cases are examined. In addition, the influences of the suspension parameters on the critical hunting speeds evaluated via the linear and the nonlinear creep models respectively are studied. Furthermore, the influences of the suspension parameters on the critical hunting speeds evaluated via the fourteen degrees of freedom car system and the six degrees of freedom truck system, which the motion of the tuck frame is restricted by a virtual boundary, are compared.