A two-degree-of-freedom vehicle wheel-rail impact vibration system model was developed, and the equivalent impact stiffness and damping of the rail were fitted by applying ABAQUS, taking into account the high and low irregularity generated by the welded joints of the rail. A wheel-rail periodic interface with fixed impact was selected as the Poincaré map, and the fourth-order Runge–Kutta numerical method with variable step size was used to solve the system response. The dynamic characteristics of the system were investigated using a combination of the bifurcation diagram, phase plane diagram, Poincaré map, time-domain diagram, and frequency-domain diagram. It was verified that the vehicle wheel-rail impact vibration system has Hopf bifurcation, Neimark–Sacker bifurcation, period-doubling bifurcation, and boundary crisis, and rich and complex nonlinear dynamic behavior changes exist. Research on the bifurcation and chaos characteristics of vehicle wheel-rail impact vibration systems can provide a reference for improving the stability of vehicle operation in engineering practice, as well as the prediction and control of chaos in vehicle vibration reduction design.