The existing vehicle adaptive cruise control mostly focuses on a single trajectory tracking target， and the key to determin the practical application benefit of the control technology is the energy-saving performance of the system. In order to ensure the tracking error's convergence and fuel economy at the same time， this paper studies a design method forof vehicle energy-saving adaptive cruise controller. Firstly， a state feedback control law with time-varying feedback gains is designed with trajectory tracking as the goal. Secondly， taking the feedback gain as the optimization variable and the accumulation of the fuel consumption per unit displacement of the own vehicle at each sampling time in the entire prediction time domain as the cost function， an energy-saving control algorithm is designed based on the economic model predictive control method， and the selection range of the feedback gain to ensure that the tracking error converges at an exponential speed is proposed. Finally， the effectiveness of the controller design is verified by numerical simulations， and the effectiveness of the method proposed in this paper in reducing fuel consumption is quantitatively demonstrated.