The gyroscope free micro inertial measurement unit/global positioning system (GFMIMU/GPS) Integrated navigation system has many advantages compared with the traditional MIMU/GPS Integrated navigation system, such as high dynamic rang, light weight, low cost and little power consumption. Undoubtedly, it will have wider applications in military and commercial fields. Aiming at the requirement of high estimation precision and real time in the real application, a method of extended Kalman filter based on model error predictive(MEP-EKF) was used for GFMIMU/GPS Integrated navigation system data fusion. The simulation results show that this method has better precision of the azimuth than that of EKF and unscented Kalman filter (UKF). Furthermore, MEP-EKF needs less computation time than UKF, only 10 percent of UKF.