Abstract: Integrated energy system (IES) is one of the effective ways to achieve the goal of "double carbon". To further reduce IES carbon emissions and total operating costs, an IES optimal scheduling model that combines supply and demand flexible demand response (DR) with a stepped carbon trading mechanism is proposed in this paper . Firstly, a stepped carbon trading mechanism is introduced to effectively reduce IES carbon emissions. Secondly, a flexible DR model of supply and demand is established, which encourages users to change their energy consumption mode through DR on the demand side and promotes the consumption of renewable energy. Finally, the effectiveness of the proposed optimal scheduling model is verified by an example analysis. The experimental results show that the proposed optimal scheduling model can effectively improve the flexibility of IES energy consumption and promote the low-carbon economic operation of IES.