This paper discusses the financing strategy and green production investment decisions within a green supply chain consisting of a capital-constrained manufacturer and a retailer. The paper first develops a game model between the manufacturer and the retailer based on the manufacturer’s investment strategies and financing choices, including bank financing and retailer credit financing. Then, a comparative analysis is conducted on the optimal financing decisions of the manufacturer between the two choices. The results show that with sufficient initial capital, the manufacturer opts for green production. In scenarios with insufficient initial capital, the optimal financing-investment strategies are contingent upon financing rates, initial capital, and investing effects. When the manufacturer selects common products, the requirements for financing interest rates in bank financing are more relaxed. The requirements for financing interest rates of retailer credit financing are more relaxed when green products are selected. In addition, the manufacturer tends to select retailer credit financing when the difference in financing rates is small or when the initial capital is limited. Moreover, the choice of financing format for green products should also factor in the investment effect. Finally, the paper explores the manufacturer’s hybrid financing strategy and operational strategy when producing two types of products.