With the development of electric vehicles, electronic hydraulic brake system becomes a hot spot of present research. In this paper，a new type of integrated electronic hydraulic brake(I-EHB) system is introduced, which is mainly composed of a motor, a worm gear, a worm, a gear, a rack etc. Motor and mechanical structure can cause friction, which leads the system to the creeping phenomenon and the dead zone. These phenomenon seriously affect the response speed and the hydraulic pressure control .In order to realize the accurate hydraulic pressure control of I-EHB system, a new friction compensation control method is proposed based on LuGre dynamic friction model. Because of the external interference or the abrasion of the system, the main parameters will change over time. So the adaptive control is of great importance. The theoretical design of adaptive control method is designed based on the feedback of the master cylinder pressure and the operating state of the system. And the stability of the control method is proved by Lyapunov theorem. A co-simulation model is built with Matlab/Simulink and AMESim, so as to prove the validity of the control method. Related experiments are carried out to track the different target signals, which is step signal, (different amplitude and frequency) sine wave signal and Artemis signal. Compared with the test result with PID control method or compensation control method based on static friction model, this method based on LuGre dynamic friction model has a definite improvement, which has advantages in response and dynamic control error. The dynamic control error at low frequency with this method is less than 1 bar. Therefore this method is an effective way to control the I-EHB system.