Integrated energy system (IES) is an important way and main starting point to achieve the goal of double carbon. In view of this, this paper constructs a low-carbon economic dispatch model for IES, including the carbon capture and storage (CCS), the two-stage power-to-gas (P2G) and the combined heat and power (CHP) unit. Firstly, at the technical level, the mathematical models of CCS, two-stage P2G and CHP are constructed for the CCS-P2G-CHP coupling system. Secondly, at the market mechanism level, the ladder carbon trading model is employed to constraint carbon emissions of IES. Finally, an optimal scheduling strategy with the objective of minimizing the total operation cost of IES is proposed, which is solved by the IPOPT solver in MATLAB. The effectiveness of the proposed model is verified by setting up multiple scenarios for example analysis, and the influence of the sensitivity of each step carbon trading parameter of the low carbon and economy of IES is analyzed.