• A method of cloud edge computing is proposed to solve the economic dispatch. • Multi-agent deep reinforcement learning is adopted to realize cloud edge computing. • The cloud server and each edge server respond to each agent. • The proposed method can protect data privacy. In view of the risks and challenges of privacy data leakage and the communication burden in the traditional economic dispatch for active distribution network with multi-microgrids, this paper proposes a cloud edge computing method for economic dispatch of active distribution network with multi-microgrids. In this method, the cloud server is responsible for the calculation of active distribution network, and each edge server is in charge of the calculation of its own microgrid. The multi-agent deep reinforcement learning is employed to realize cloud edge collaborative computing, where each edge server and cloud server corresponds to an agent. Through case analysis, the reliability of the cloud edge computing method is confirmed. The simulation results show that the proposed method can provide a high-quality solution for economic dispatch of active distribution network with multi-microgrids on the premise of protecting data privacy and reducing the communication burden.