The intermittency of renewable energy poses challenges on the reliable and economical operations of microgrids. This paper considers a grid-connected microgrid model which consists of a logistics distribution system, where electric vehicles (EVs) depart from the depot, deliver the goods to multiple demand loads, and then, return to the depot. Based on this, this paper studies the coordinated dispatch strategies of EVs to smooth renewable energy and load fluctuations of the microgrid while ensuring the quality of logistics services. A microgrid operation model is proposed to optimize the driving routes, fast-charging time, and regular-charging/discharging strategies of EVs. Specifically, the objective is to minimize the overall operation cost of the microgrid while satisfying the requirements of the logistics distribution tasks. A self-adaptively imperialist competitive algorithm is proposed to solve the model. The simulation results demonstrate the effectiveness of the proposed model.