This paper presents a model matching control (MMC) method based on the sliding mode control (SMC) method for longitudinal acceleration tracking control in a vehicular stop-and-go cruise control system. The nonlinearity of the vehicle acceleration response at low speeds was analyzed to develop a transfer function model of the vehicle longitudinal dynamics using the least-mean-square system identification technique. This transfer function was then used to design the MMC controller, including an SMC feedback compensator. The system combines the advantages of the two control methods with robust control and rapid response. Simulations show that the controller enhances the rapid trackability to the vehicle acceleration and improves the system's robustness at low speeds compared with conventional PID MMC controllers.