Integrated energy system (IES) has been widely used in the field of energy supply due to the high efficiency of energy utilization. However, its economic operation is challenged by different uncertainties in the system. This paper establishes a multi-stage robust optimization model for IES with both decision-independent uncertainties (DIUs) and decision-dependent uncertainties (DDUs). Because some uncertainties in IES are affected by the decision, such as the price, they are modeled as DDUs. To solve the complicated scheduling problem with DDUs, an improved column-and-constraint generation (C&CG) algorithm is proposed. Finally, a 33 nodes system with 24 time slots is utilized to verify the efficacy of our design.