The challenge of energy conservation and emission reduction makes the energy management research for zerocarbon communities (ZCCs) quite important. In this context, a Stackelberg game based energy sharing model for ZCC considering the reward and punishment of carbon emission is proposed. Firstly, a framework of ZCC including a ZCC operator (ZCCO) and multiple building prosumers (BPs) is established. To improve the energy conservation and emission reduction of ZCC, two reward and punishment mechanisms respectively from shortterm and long-term perspectives are introduced. In the day-ahead scheduling stage, the scheduling model of energy storage systems (ESSs) considering the economy and environmental protection is established. Especially, the ESS is scheduled by ZCCO to further reduce the overall carbon emission. In the real-time optimization stage, considering the reward and punishment mechanisms for carbon emission, benefit functions of ZCCO and BPs are constructed and modified accordingly. Then, the Stackelberg game model of the ZCC considering BPs and ZCCO is constructed based on the internal prices from ZCCO. The energy sharing among BPs is also realized. Finally, the proposed model is solved by the particle swarm optimization algorithm and CPLEX. Simulation results show the proposed model and algorithm are reasonable and effective in the energy sharing.