The control forms of the vehicle have transformed from hydraulic or mechanical control to electrical control owing to the increasing demand of automotive safety and soaring development of electronic technology. Compared with the traditional mechanical parking brake system, the electrical control of brake named Electrical Parking Brake (EPB) System presents a variety of advantages. What's more, it shares common actuators and realizes the communication between electrical control systems to advance the vehicle industry to intellectualization.With such superiority, the EPB System has aroused much interest. But the difficulty in building the simulation model lies in the description of friction in screw-nut system of which the nonlinear component causes the hysteresis. However, almost all models found in the literature before are the static friction model with the limit of description of dynamic features like pre-sliding frictional features and parameters variation.A method to describe the friction feature is proposed based on the LuGre dynamic friction model in this paper. In contrast to the static friction model, the paper demonstrates the LuGre model's advantages over the Stribeck model. In addition, the parameters in friction model are variable with the factor of the position change of the mechanism, asymmetrical surface roughness and the influence of environmental temperature change should also be taken into consideration. Therefore an adaptive friction controller is designed. And the Stability Theory of Lyapunov is also applied to prove the global stability of the system. Finally, the effectiveness of this method by the simulation of the EPB System is verified.