Considering the influence of the time factor on product greenness and brand goodwill, the differential game method is introduced to study the business model selection and marketing strategy of upstream and downstream enterprises in a green supply chain under the dynamic framework. The differential game models of independent marketing and joint marketing under the resale model and the platform model are established respectively, and the corresponding equilibrium results are solved and analyzed. The results show that regardless of whether the resale model or the platform model is adopted, the joint marketing is the optimal marketing strategy for the manufacturer and the retailer. When the manufacturer and the retailer reach an agreement on joint marketing, the platform model is the optimal strategy for the retailer, while for the manufacturer, the choice of the business model is related to the commission ratio of the platform model. Specifically, when the commission ratio is low, the manufacturer tends to choose the platform model, and when the commission ratio is high, the manufacturer tends to choose the resale model. In general, the result of the game between the manufacturer and the retailer is the platform model with low commission ratio and joint marketing.