To ensure lateral stability during the cruising of a differential steering vehicle (DSV), this paper presents a curving adaptive cruise control (ACC) system coordinated with a differential steering control (DSC) system, which considers both longitudinal cruising capability and lateral stability on curved roads. Firstly, a DSV dynamics model is developed and a control strategy architecture for a curving ACC system is designed. Then, the car-following control strategy for the curving ACC system is designed based on the fuzzy model predictive control (FMPC) algorithm. The strategy aims to improve the economy and balances car following, safety, comfort and economy. Moreover, fuzzy logic rules are designed to update the weight coefficients of the performance indicators in real time. Finally, the lateral stability controller is designed based on the preview algorithm and the sliding mode control (SMC) algorithm. The simulation results show that the lateral stability of the DSV during the curving cruise is realized via the control of the differential drive torque of the two front wheels. The proposed FMPC controller and SMC controller based on the preview control algorithm satisfy the performance in terms of vehicle following and lateral stable driving in the process of cruising.