Implementing the overall goal of carbon emission reduction and allocating it to specific enterprises under the premise of coordination of interests is not only an important step and link of the development of carbon trading market but also a necessary guarantee for implementing China's overall goal of carbon emission reduction. In this paper, total quantity control of and trading conditions for carbon quota for coal-fired power supply chain enterprises were introduced based on the framework of the Stackelberg model and with the carbon quota constraints being taken into account, a coordination game model of carbon emission reduction of coal-fired power supply chain enterprises was constructed, and a revenue sharing coordination mechanism among supply chain enterprises were designed. In this coordination mechanism, the revenue sharing contract coordination game mechanism in coal-fired power supply chain was designed first on the basis of analyzing the coal production quantity and coal ordering quantity of the coal and electric power enterprises in their decentralized and centralized decision-making and their respective carbon emission reduction and profit situations without contract. And then, the implementation conditions for this revenue sharing contract coordination game was further analyzed, in other words, under the condition that the decision-making level of the coal and electric power enterprises should be equivalent to the centralized decision-making level without contract, it was guaranteed that the profits and carbon emission reduction levels of the coal and electric power enterprises under the revenue sharing contract were greater than under decentralized decision-making without contract, and the global coordination of coal-fired power supply chain was realized. The data calculation examples and parameter sensitivity analysis further verified the results of the theoretical analysis.