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The aim of this paper is to establish a simple and accurate nonlinear model of a yaw damper for the dynamic numerical simulation of high-speed trains. An improved nonlinear yaw damper model is proposed based on the traditional Maxwell model. It comprises a piecewise linear force–displacement spring and a piecewise linear force–velocity damper in series. These nonlinear inputs for the model are retrieved from the dynamic performance tests of the damper, and the force–displacement and force–velocity curves are further modified to improve the modelling accuracy according to the test results. The proposed model can accurately simulate the damper's dynamic stiffness and dynamic damping characteristics with respect to the excitation frequency or displacement, which cannot be reproduced when using the traditional Maxwell model. Both the traditional Maxwell model and the improved nonlinear model presented in this work are integrated into a multibody dynamics railway vehicle model to simulate the typical dynamic problems of a high-speed train operating at 250 km/h in northeast China. Through comparative analysis, it was found that the numerical simulations are consistent with the field measurements. It can be concluded that the proposed nonlinear damper model is more suitable for studying railway vehicle system dynamics under various operating cases. By contrast, the input parameters of the traditional Maxwell model must be modified artificially according to the vehicle responses and the dynamic characteristics of the yaw damper.