Trajectory tracking is a critical part for a tracked unmanned ground vehicle (UGV) that works in the off-road environment. In order to improve the controller adaptability and accuracy, our study proposes a combination of the Extended Kalman Filter (EKF) and Model Predictive Control (MPC). Aiming at the tracked UGV, the MPC adopts a vehicle dynamics model with kinematics relationship to generate the expected motor torque. Compared with kinematics-based motor speed controller, our MPC-based system responses faster and more accurately. Then, the EKF is utilized to estimate the road resistance coefficients in real time, strengthening the MPC adaptability to the uncertain road conditions. The proposed system is verified by a real electric tracked UGV with off-road conditions. The experimental results show that the EKF-MPC-based motor torque controller can adapt to the unstructured environment well and achieve a better tracking performance than the MPC-based motor speed controller. Significantly, the lateral tracking accuracy is improved by 24% when steering.