Abstract: In the context of the Carbon Emission Peaking and Carbon Neutrality, it is important to promote the low-carbon transformation of the traditional power systems. This paper focuses on the impact of multiple carbon-source-load uncertainties on the low-carbon economic operation of an integrated energy system, and proposes a two-stage robust optimization operation. Firstly, the uncertainty of the electricity indirect carbon emission intensity at the integrated energy system junction point is analyzed, and the polyhedral uncertainty set is used to model it. Secondly, a mathematical model is established for the equipment aggregated by the integrated energy system, and a carbon emission trading mechanism is introduced to analyze the equipment operation cost and the carbon emission cost. Then, using the column-and-constraint generation (C&CG) algorithm, the two-stage robust optimization model is decomposed into a master problem and a sub-problem for the cyclic solution. Meanwhile, the Karush-Kuhn-Tucker (KKT) condition and the big-M method are used to simplify and linearize the lobule-layer structure and the nonlinear terms existing in the sub-problem. Finally, the validity of the proposed model and the solution algorithm is verified through case studies. In addition, the low-carbon economy and the ability to withstand fluctuations of the uncertainties of the proposed robust optimization method for the integrated energy system are dissected.