Integrated energy system (IES) are an effective way to solve energy loss and environmental pollution problems. A consensus-based distributed dispatching method is studied to realize economical operation and the environmental protection of IES. First, a stepped carbon trading mechanism is studied, where a non-linear cost coefficient that increases with the carbon emission interval is designed to construct the carbon trading cost function. In this way, the amount of carbon emission is limited. Second, the power loss problem in the energy transmission process is considered, and a supply-demand balance constraint that combines energy demand and transmission loss is constructed. Third, the incremental costs of electricity, heat, and gas supply units are considered as the consensus variables. Then, a leader-following consensus algorithm is designed to perform the distributed scheduling of the IES, thus realizing the optimal output of energy supply for each unit. Finally, the effectiveness of the proposed low-carbon economic dispatching strategy is verified with some numerical experimental cases.