In this study, we address the trajectory tracking control problem of a hydraulic-driven skid-steer mobile robot. A hierarchical control strategy is proposed to simultaneously consider the robot’s position control and the velocity control of the hydraulic motors. At the upper level, a nonlinear model predictive control (NMPC) method is employed to control the position and heading of the mobile robot. The NMPC controller takes into account the robot’s physical constraints and generates the desired robot motion velocity. Then, to control the hydraulic drive system, a current–velocity mapping-based control method is introduced. By establishing the mapping relationship between the control current applied to the hydraulic motor and its corresponding output velocity, the dynamics of the hydraulic motors are characterized. Consequently, the lower-level controller can directly obtain the control signal for the hydraulic actuator through lookup mappings. Additionally, PID controllers are adopted to compensate for velocity tracking errors. The proposed hierarchical control strategy decouples the robot’s position control and the hydraulic system control, simplifying the overall controller design, leading to improved control performance. To validate the effectiveness of the proposed control strategy, several experiments were conducted on a hydraulic-driven skid-steer mobile robot, and the results demonstrate the effectiveness of the proposed approach.