Under the "dual-carbon" goal, the energy industry is facing many challenges such as the level of technological development, the tight timeframe for carbon reduction, structural transformation and environmental governance, so integrated energy system (IES) plays an important role in realizing a new power system. Considering the ladder-type carbon trading mechanism and demand-side response, a low-carbon economic operation optimal scheduling model for IES is proposed. Firstly, gas load emission factor is introduced into the carbon emission model, and the ladder-type carbon trading mechanism is adopted. Then, based on the time-of-use price and substitution of each energy source, two types of demand-side response, price-based and substitution-based, are investigated separately. Finally, with the objective of minimizing the integrated cost, the simulation results show that the model that takes into account the ladder-type carbon trading mechanism and demand-side response, and considers the impact of gas load emission, can significantly reduce carbon emission of IES. After demand response, the energy purchase cost, carbon trading cost and carbon emission are reduced by about 3.38%, 36.25% and 18.52%, respectively.