The paper deals with the design of adaptive cruise control by integrating longitudinal motion control and a safety logic control. The proposed control algorithm consists of an inner loop to manipulate the brake pedal and throttle opening position, and an outer loop to maintain the safe distance from leading vehicle. A multistage local linear model is identified using least squares method to describe nonlinear dynamic of longitudinal motion model. The objective of multistage model based predictive control is to minimize square of longitudinal vehicle speed error and square of brake pedal and throttle torque through receding horizon. By using the proposed control algorithm, the predictive control problem is still maintained as a quadratic programming problem. The safety logic control is designed base on the reference value of vehicle speed and distance from heading vehicle. Simulation results are given to demonstrate the effectiveness of the proposed control strategies.