Abstract: With the increasing requirements of green energy transition, in order to achieve the low-carbon economic dispatching of the integrated energy system, it is increasingly worthwhile to explore the carbon reduction potential on the demand side, in addition to considering carbon reduction strategies on the source side. By taking into account the source and load, an optimal dispatching model of integrated energy system considering the low-carbon demand response and supply-demand Stackelberg game is proposed. Firstly, the carbon trading mechanism is considered on the supply side, and the carbon emissions on the supply side are transformed to the load side by using the carbon emission flow model. Secondly, considering the carbon emissions from the perspective of user side, the incentive-based low-carbon demand response model is proposed to guide the low-carbon dispatching on the supply side. Thirdly, the Stackelberg game model is used to form an interaction between the supply side and the user side, obtaining a reasonable and effective incentive scheme to further explore the carbon reduction potential on the user side. Finally, the effectiveness of the proposed method is verified by case simulation results, which reduces the system carbon emission while ensuring the economy.