Aiming to realize the economical and low-carbon operation of the integrated energy system (IES), this paper proposes a low-carbon optimal dispatch strategy incorporating a reward-and-punishment tiered carbon trading mechanism and integrated demand response (IDR). First, in order to significantly improve energy utilization, a multi-energy complementary optimal dispatch model is established. Based on this, an integrated demand response model for multi-energy loads and its response compensation mechanism are further proposed. Second, introduce a tiered carbon trading mechanism into the optimal scheduling model, and construct IES objective function. The output of wind power and photovoltaic is uncertain, so the Latin Hypercube Sampling (LHS) was used to generate typical scenarios for wind and light output. Finally, use MATLAB software to linearize the original problem, and solve the proposed model using the CPLEX solver. This article sets up three scenarios for comparative analysis. The results show that the put forward strategies successfully balance the economic and environmental benefits of the system.