Abstract: To enhance energy efficiency and reduce carbon emissions, an integrated energy system (IES) which incorporates carbon capture and power-to-gas equipment, is constructed. The introduction of a carbon trading mechanism is made and a two-stage optimization method for IES with heat-supply network loss taken into account is proposed. The first stage involves optimizing the flow rate of the heat-supply network and the temperature of the supply and return water, with the goal of minimizing the heat supply from the heat source, considering of the loss of the thermal network. In the second stage, based on the optimized heat supply in the first stage, the output of each unit is optimized under the premise of meeting various constraints, with the goal of minimizing the system operating cost and carbon trading cost. An integrated energy system model, consisting of six-node power grid, four-node gas network and six-node heat-supply network is simulated. Compared with the comparison scheme, the proposed model demonstrates a 15.5% reduction in total daily operating cost, along with a significant decrease of 39.5% in carbon emissions, thereby verifying its effectiveness.