Abstract: The master-slave game method shows the internal interest relationship of the upper and lower levels more clearly, and plays an important role in improving the internal economy of the integrated energy system. Aiming at the inconsistency of the interests of each Stakeholders in integrated energy systems and the contradictory problems of low carbon and economy, a stepped carbon trading model of the integrated energy system is proposed. Aiming at the inconsistency of the interests of each Stakeholders in integrated energy systems and the contradictory problems of low carbon and economy. First, a stepped master-slave game carbon trading model is constructed to consider the benefits of different participants and the overall carbon trading objective; Second, an adaptive differential evolutionary algorithm is proposed to solve the master-slave game to obtain the global optimal solution, which utilizes orthogonal test method to initialize the population in order to improve the adaptability to the uneven distribution of stochastic individuals; at the same time, adaptive variation operators are introduced to maintain the diversity of the individuals and to avoid falling into local optimality. Finally, the multi-area integrated energy system constructed based on the IEEE 33-node model is simulated and verified, which shows that the proposed model has better performance and efficiency. It is expected to provide a new way for the integrated energy system with low green carbon and double economic benefits.