Rail corrugation is the undulating wear on the surface of the rail, which has a fixed wavelength at a certain speed and will bring vibration and noise problems to the train-track system, resulting in the failure and shedding of system components and seriously affecting the safety and comfort of train operation. At present, the most effective measure to control rail corrugation is rail grinding. Determining the grinding limit of rail corrugation is the key to formulating an economical grinding strategy and implementing a grinding plan. Determining the grinding limit requires a systematic and in-depth study of the transient response of the wheel-rail system under rail corrugation excitation. The dynamic response of vehicle-track system under rail corrugation excitation is mainly studied by two methods of vehicle-track system dynamics model based on multi-body system dynamics theory and wheel-rail transient rolling contact model based on finite element. However, most of the vehicle-track system dynamics models based on the multi-body system dynamics theory assume that the wheel-rail contact is steady-state, which cannot consider the effect of the real wheel-rail contact geometry, and the wheel-rail contact is unsteady under the rail corrugation excitation. The traditional transient rolling contact model of the wheel-rail system based on finite element has a large initial disturbance and a long dynamic "relaxation zone", which further increases the element law of the model. A transient rolling contact model of the wheel-rail system of high-speed railway was established. An improved simulation scheme for the wheel-rail transient rolling contact was proposed, in which the rotation speed of the wheelset was applied in a static analysis based on mixed Lagrangian/Eulerian description to obtain the steady-state contact solutions. The improved method could avoid the initial disturbance caused by applying the rotation speed to the wheelset in a dynamic analysis. Based on the improved method, the variation characteristics of the wheel/rail vertical force, the longitudinal force and the stresses in the contact patch under the excitation of rail corrugation were studied. The effect of the wavelength and depth of rail corrugation on the transient response of the wheel-rail system was discussed. The improved method could provide a stable contact solution at the expense of a shorter dynamic relaxation zone. When the speed increased to 500 km/h, the required length of the dynamic relaxation zone was only 1 250 mm. Corrugation aroused strong wheel-rail dynamic interaction and the vertical and longitudinal wheel/rail force vibrated at the same frequency but with a phase difference. When the wheelset passed through the position between the crest and the trough of the corrugation, the center of the contact patch shifted to side close to the corrugation geometry. The deeper the corrugation, the stronger the dynamic wheel/rail forces. The peak and valley values of the vertical and longitudinal forces have a linear relationship with the corrugation depth. When depth of the corrugation with a wavelength of 65 mm increases to 105 μm, the wheel load reduction is 0.65. There is no simple linear relationship between the wavelength of the corrugation and the amplitude of the dynamic wheel-rail forces. Under the excitation of the corrugation with the wavelength of 65 mm and 125 mm, the vertical and longitudinal wheel-rail forces show the characteristics of single wavelength.