An integrated system for path planning and tracking control was developed to address the structural mismatch between the discrete path generated by the A^* algorithm and the continuous inputs required by multi-reference point model predictive control (M-MPC), and to improve the tracking accuracy and smoothness of path tracking control. The A^* reference path was smoothed and discretized at equal arc-length intervals, and the generated reference point sequence was introduced into the prediction horizon of the M-MPC controller. A heading alignment mechanism was designed to mitigate the problem of large initial heading deviations between the reference path and the differential-drive robot, thereby ensuring a seamless transition from path planning to tracking control. Experimental results demonstrated that the proposed system achieved high accuracy and smoothness. Compared with the direct combination system of the A^* algorithm and M-MPC, the peak and average values of the displacement error were reduced by 51.85% and 20.40%, respectively, while the cumulative control increment was decreased by 28.86%. Compared with the systems combining the smoothed A^* algorithm and a pure pursuit controller or a single reference point MPC, the peak and average values of the displacement error was decreased by at least 52.80% and 41.58%, respectively. The proposed system improved the tracking accuracy and smoothness, and enhanced the motion control performance of differential-drive robots in complex environments.