Regional energy internet (REI) contains massive market agents, whose interests and objectives vary from each other. In consequence, it is challenging to stimulate the energy conservation and emissions reduction participation of each agent by the conventional schedule optimization method. This paper proposes a multi-agent schedule optimization method for REI considering the improved tiered reward and punishment carbon trading model. Firstly, the energy flow constraints and device constraints of REI are established. Secondly, to tighten restrictions on carbon emissions, the relative carbon emission is used as the criterion to establish the improved tied reward and punishment carbon trading model. Next, to analyze the real multi-agent game situation in the market, different agents are classified, and the objective functions are defined based on their revenue. Finally, a two-layer algorithm is used to solve the above multi-agent model. Simulation results verify that the proposed method can effectively reduce carbon emissions and significantly enhance the revenue of the region.