The paper considers an emission-dependent supply chain consisting of one single emission dependent manufacturer and one single emission permit supplier in the government's ‘cap-and-trade’ regulation. The system will not only be influenced by product carbon footprint and government carbon emissions caps, but also affected by the carbon price decision of the upstream supplier. By the establishment of the two agents Stackelberg game model, their mutual reflecting Nash equilibrium solution can be obtained. On this basis,we discuss and analyze the relationships between product carbon emission, government's ‘cap-and-trade’ regulation and optimal solution. The results show that the impact of unit product's carbon emission and the government's ‘cap-and-trade’ regulation on two agents' profit is inversed. Product's carbon emissions and government's carbon regulation can both provide an improvement space for the two agents to get more profits. Manufacturers should effectively control product's carbon emissions, and governments should reasonably determine carbon emissions cap. Only in this way can make the increment of the two agents' utility optimal. At last, a numerical experiment is given to prove the validity of the developed models and policy by selecting reasonable data.