In view of the high energy consumption and pollution problems facing economic and social development in China, an integrated energy system (IES) provides a new way to solve problems such as energy efficiency and environmental pollution. At the same time, flexible coordination of the output of various pieces of equipment in the system is key to realizing low-carbon and economic operation. To further explore the IES in terms of dispatch potential in economic operation and low-carbon environmental protection, an IES low-carbon economic dispatch model is proposed. First, this paper establishes an IES model including photovoltaic, wind power, gas-fired units, various types of energy storage, carbon capture and power-to-gas equipment. It then combines the coupling relationship and flexibility characteristics between electricity, gas, and heat load energy conversion to construct a comprehensive demand response model. Second, it considers IES joining the carbon trading market, and introduces a stepped carbon trading cost model to restrict system carbon emissions. Finally, the optimization goal is to minimize the comprehensive operating cost of the system including energy purchase, carbon emission-related and demand response compensation costs. CPLEX software is used to simulate various operation scenarios, and the results show that the proposed model can effectively reduce the system operation cost and carbon pollution emissions. This work is supported by the General Program of National Natural Science Foundation of China (No. 51777155).