Dynamic optimization about vertical cooperation on carbon emissions reduction is discussed based on the differential game in a low-carbon supply chain consisting of a single supplier and a single manufacturer. Stackelberg differential game models are built under a supply chain in which the manufacturer is a leader and the supplier is a follower. The optimal feedback equilibrium strategy with long-term cooperation of the supplier and the manufacturer about reducing emissions and their own optimal value function of profits can be obtained respectively, and the optimal trajectory of products’ carbon emissions also can be found. Finally, through a numerical example, it is analyzed how the long-term cooperation strategies on carbon emissions reduction of manufacturer and supplier affect the carbon emissions of product, and the theoretical basis is provided for long-term emissions reduction vertical cooperation in supply chain.