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Distributed integrated energy system (DIES) will become the main energy supply method for end-users, however, the volatility of renewable energy makes energy consumption more difficult. To address the problem, this paper proposed an optimization method of DIES energy transaction based on Stackelberg game. Firstly, the typical structure of DIES is studied and a energy transaction framework of electric-heat energy is proposed by introducing integrated energy operator(IEO); secondly, with IEO as the leader and DIES as the follower, considering the highest profit of IEO and the lowest cost and carbon emission of DIES as the objectives, and combining the operational constraints of different subjects, a one-master-multiple-slave Stackelberg game model is established; thirdly, the existence of Nash equilibrium of this game model is demonstrated, and a solution algorithm based on Particle swarm optimization nested Non-dominated Sorting Genetic Algorithm-II is proposed; Finally, to verify the validity of this model, two modes are designed and simulated, and the results show that the proposed method can improve the renewable energy consumption by 2.92%, reduce the DIES energy cost by 3.94%, and reduce the interactive power with the grid by 30.91%, while the sensitivity analysis shows that the method can better cope with energy price changes. • The main contributions of this paper can be summarized as follows: • Analyzed the typical architecture of DIES and proposed a new energy trading framework. • A Stackelberg game model with IEO as the leader and DIES as the follower is developed. • The solution algorithm of PSO nested NSGA-II is proposed. • This method can reduce the cost of energy use and increase the consumption of renewable energy. [ABSTRACT FROM AUTHOR]