To analyze the influence of the leaf spring hysteresis characteristics on the vehicle body vibration performance, it is necessary to take the physical nonlinear factors into account in the suspension dynamic modeling analysis. The hysteresis characteristics of the leaf spring are caused by the contact and friction between the spring pieces. Besides that, the damping elements of the suspension system are also strongly nonlinear. And hence this article presents a generalized Maxwell-slip damper (GMD) model, which can represent the general hysteresis characteristics of the suspension system. The GMD model incorporates spring stiffness and nonlinear damping in addition to spring friction using the Maxwell model. Then the effects of various parameters on the hysteresis characteristics of GMD model are analyzed and verified by simulation and bench experiments. In addition, an eight degree of freedom (8-DOF) full vehicle model capturing some frictional characteristics was established to study vehicle vibration performance under random road excitation. At the same time, the actual vehicle test is conducted under different road conditions. Ultimately, the results of the nonlinear suspension model have a reasonable agreement with the experimental results, which further demonstrates the credibility of the proposed GMD model. That is, the full vehicle dynamic model with friction force is entirely accurate and useful. The proposed nonlinear hysteresis model may be instructive for accessing the vehicle vibration response to further study the direct effects of friction on vehicle handling and driver feedback.