In order to achieve the low carbon operation and economic benefits of integrated energy system (IES) in electrolytic aluminum, a low carbon economy operation strategy considering the demand response (DR) and equipment capacity optimization is proposed. First, an IES topology integrating electricity and heat energies is established, and a DR model is also established based on the transferability of electricity and heat loads. Then, the IES carbon emission accounting model is established, and a ladder-type carbon trading mechanism is introduced to implement the restriction of carbon emission. Finally, the optimization operation model is transformed in the form of mixed integer linear problem, which considers the comprehensive costs of energy purchase, equipment operation and maintenance, carbon trading, equipment investment and wind and light abandonment, and is solved by CPLEX. Experimental results show that when DR is considered, the total operation cost and carbon emissions are reduced by 3.07% and 1.17% respectively. In addition, after further considering the optimization of equipment capacity, the total operating cost and carbon emission can be additionally reduced by 0.39% and 0.64% respectively, while the production of electrolytic aluminum is ensured. As discussed above, the method proposed can improve the economy and environmental performance of IES operation to a certain extent.