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Energy-saving and emission reduction will become the focus of the energy industry in the future. The coordination of the carbon and electricity markets can help achieve the goals of carbon reduction. With the establishment of the carbon market, carbon emitting power generation units (CEPGU) need to consider the trading strategy and comprehensive benefits in the electricity and carbon markets. To further explore the mechanism and interaction process of electricity price and carbon price, the day-ahead electricity market model and carbon market trading model are developed in this study. Based on the deviation between the bid-winning power output in the electricity market and the quota plan in the carbon market, the generation cost model and the carbon quota trading decision model of the units are constructed. Finally, a case study is provided to simulate the coordinated trading process of the carbon and electricity markets. The transaction time scales of the two markets are matched. The results prove that the generation plan of the units can coordinate with the carbon quota level and provide a trading strategy for the power generation enterprises.