Regarding the different ownerships and autonomy of microgrids (MGs) in the distributed multi-microgrid (MMG) system, this paper establishes a multi-stage energy scheduling model based on a multi-agent system (MAS). The proposed mechanism enables a microgrid agent (MGA), a central energy management agent (CEMA), and a coordination control agent (CCA) to cooperate efficiently during various stages including prescheduling, coordinated optimization, rescheduling and participation willingness analysis. Based on the limited information sharing between agents, energy scheduling models of agents and coordinated diagrams are constructed to demonstrate the different roles of agents and their interactions within the MMG system. Distributed schemes are introduced for MG internal operations considering demand response, while centralized schemes under the control of the CCA are proposed to coordinate MGAs. Participation willingness is defined to analyze the MGA’s satisfaction degree of the matchmaking. A hierarchical optimization algorithm is applied to solve the above nonlinear problem. The upper layer establishes a mixed-integer linear programming (MILP) model to optimize the internal operation problem of each MG, and the lower layer applies the particle swarm optimization (PSO) algorithm for coordination. The simulation with a three-MG system verifies the rationality and effectiveness of the proposed model and method.