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This paper proposes an economic optimal scheduling method of based on the stackelberg game theory to address the energy trading of distribution network(DN) with multi-microgrid （ MMG ） . First, the optimal scheduling process is designed as a one-leader N-follower stackelberg game. The equilibrium solution of the game is solved by the mixed integer programming (MIP) and differential evolution (DE) algorithms. The distribution network operator (DNO) is taken as the leader, and the microgrid operator (MGO) is regarded as a follower, aiming at the minimum operation cost. DNO encourages MGO to participate in energy trading by setting internal transaction price; MGO makes energy storage and load decision in response to internal transaction price, and then affects the price strategy of DNO through the net load. Moreover, the power flow of distribution network is constrained to ensure its safe and stable operation. Finally, an example analysis of the improved IEEE 33-bus system is designed to proof the effectiveness of the presented energy trading method.