With the spread of O2O business model and the carbon cap-and-trade mechanism has been widely recognized and applied in many countries, this paper studies the manufacturer and retailer's price decisions, as well as coordination problems for the O2O business model under the carbon cap-and-trade mechanism by using game-theoretic formulation. The centralized and decentralized decision-making models for O2O mixed channel supply chain are established, and the combinations of optimal pricing strategies for the manufacturer and retailer are obtained respectively under the two decision-making styles. Moreover, the two-part tariff contract is introduced to coordinate the O2O mixed channel supply chain system with carbon cap-and-trade mechanism. Besides, the effects of the carbon trading price on pricing strategies, coordination mechanism and profits of the O2O mixed channel supply chain members are also analyzed. Finally, a numerical example is provided to confirm the correctness of the conclusions, and some other managerial highlights were also discussed in this paper.