To fully consider the low-carbon nature of an integrated energy system and the complex response characteristics of multi energy load, an energy hub (EH) master-slave game optimal scheduling strategy considering the integrated demand response and reward and punishment ladder carbon trading mechanism is proposed. First, to effectively evaluate the flexible characteristics and response capacity of multi energy load, a building heat transfer model and domestic hot water storage model are integrated into the building EH model. Then a refined integrated demand response model considering various heat disturbance factors is constructed. Secondly, considering the green regulation ability of the supply and demand sides, this paper constructs a reward and punishment ladder carbon transaction cost model. A master-slave game low-carbon optimization model for energy hub operators and users is established based on Stackelberg game theory. Finally, a differential evolution algorithm combined with a CPLEX toolbox is proposed to analyse the proposed model. The simulation results show that the proposed method can effectively limit the carbon emission of the system, give full play to the response ability and emission reduction potential of demand side resources, and realize a win-win of EH economy and environmental protection. This work is supported by the National Natural Science Foundation of China (No. 51607105).