A new longitudinal control strategy for vehicle adaptive cruise control (ACC) systems is presented.The running relationship between the ACC vehicle and the detected target vehicle is described by the relative velocity and the deviation between the actual headway distance and the prescribed safety distance.Based on this,two state space models are built and the linear quadratic optimal control theory is used to yield desired velocity for the ACC-equipped vehicle when with the target vehicle detected.By switching among four control modes,the desired velocity profile is designed to deal with different running situations.A velocity controller,which includes a PID controller for throttle openness and a neural network controller for brake application,is developed to achieve the desired velocity profile.The proposed control strategy is applied to a non-linear vehicle model in a simulation environment and is shown to provide the ACC vehicle comfortable ride and satisfying safety.