Four-wheel, independently driven skid-steer mobile robots have been widely used in some fields, such as indoor product shipping and outdoor inspection and exploration. Traditional skid-steer mobile robot controllers often use a kinematics controller to obtain the desired speed of each wheel, complete speed closed-loop control of each wheel and achieve the robot’s trajectory tracking control. However, the controller based on kinematics may lead to robot chattering and wheel spin from being directly driven by the motor on uneven grounds. To solve these problems, we developed a four-wheel, independently driven skid-steer mobile robot with a damping module for the timing-belt servo system and proposed a model-based coordinated trajectory tracking control method with the timing-belt servo system. First, the kinematics and dynamics of the mobile robot are established, including the chassis kinematics and dynamics, as well as the dynamics of the timing-belt servo system. Secondly, the hierarchical control law is designed, which has adaptive robust control of the upper-level robot chassis, middle-level control allocation approach, and adaptive robust control of the bottom-level timing-belt servo system. Finally, the proposed method is verified by the robot’s trajectory tracking control comparison simulation experiments and has a better control performance.