In order to promote the low-carbon and economical operation of the integrated energy system, this paper researches the role of stepped carbon trade and demand response strategies on optimal scheduling of the integrated electricity-heat energy system (IEHS). Firstly, the IEHS structural model, the stepped carbon trade model and the demand response model are established. Then this article establishes the IEHS optimization problem model with setting up the objective function of minimizing operating cost and a series of constraints. Finally, taking the IEHS of an industrial park as an example, a simulation model was established in MATLAB and three different scenarios were set up for simulation. The results show that the stepped carbon trade and demand response strategies proposed in this paper have obvious effects on the optimal dispatch of IEHS. They can not only effectively promote energy conservation and carbon emission reduction but also reduce the operating cost of system.