In recent years, with the development of society and economy, the ecological environment has been deteriorating day by day and people′s attention to environmental issues has been increasing. The development of green supply chain has become an inevitable choice for China to achieve sustainable development and economic structural transformation. Facing the severe environmental situation, many enterprises implement green transition to alleviate environmental pressure, but some enterprises face huge challenges in the process of green transition due to capital problems. When enterprises face capital constraints in green transition, they usually rely on BCF (bank credit financing) or TCF (trade credit financing) for financing. During the financing process, the borrowers are vulnerable to bankruptcy when they face external risks such as legal liability and regulatory penalties brought about by credit problems. This kind of risk is usually measured by “credit rating”, which is a quantitative assessment of the overall credit of the enterprise. The lender can judge the bankruptcy risk of the borrower by credit rating. Due to information asymmetry and opacity, it is usually difficult to accurately assess the credit information of the borrowers. Therefore, credit rating cannot accurately capture the real bankruptcy risk of the borrower and thus affect the reasonable decision-making of lender. With the properties of “decentralization” and “immutability”, blockchain technology provides an effective way to solve the above problems. On the one hand, the use of blockchain ensures the lender clearly and intuitively audit the borrower′s credit information and improves the accuracy of the information. On the other hand, the use of blockchain realizes product traceability and improves consumers′ green trust. Therefore, considering the impact of blockchain technology on credit rating and consumers′ green trust, it is vital to analyze the optimal prices and profits of the green supply chain members before/after they join the blockchain platform as well as to explore the financing strategies of green supply chains under different scenarios. This paper considers a supply chain consisting of one supplier and one capital-constrained manufacturer. The supplier is the Stackelberg game leader and the manufacturer is the follower. Both the supplier and the manufacturer aim at maximizing their profits and the manufacturer has limited liability. The manufacturer can obtain financing through BCF or TCF. Firstly, taking into account the consumer′s green trust and the manufacturer′s credit rating, we develop game theoretic models under BCF/TCF by considering whether the supply chain members join the blockchain platform. We first derive the optimal decisions under different scenarios. Then, we analyze the impact of crucial parameters, i.e., consumer green trust, on decision variables. Next, we discuss the conditions under which the supply chain members would join the blockchain technology platform and compare relevant variables under each scenario. Finally, we analyze the profits of different supply chain members before/after they join the blockchain technology platform under the TCF and the trade-offs between the two financing modes for different supply chain members through numerical experiments. The results reveal that: 1) The green level of the product under BCF is higher after joining the blockchain platform. 2) Under TCF, the magnitude of the green level of the product before and after joining the blockchain platform is related to the displayed bankruptcy risk before the manufacturer joined the blockchain platform, the changes in the displayed bankruptcy risk after the manufacturer joined the blockchain platform, and the green investment cost coefficient. 3) Under BCF, whether the supply chain members join the blockchain platform depends on the changes in the displayed bankruptcy risk after the manufacturer join the blockchain platform. Similar conclusions can be observed under TCF. 4) Whether the supplier provides TCF is related to the interest rate under these two financing modes. 5) When the interest rate of BCF is smaller than that of TCF, the manufacturer will choose BCF. We obtain the following managerial insights: 1) In the context of low-carbon and environmental protection, small and medium-sized enterprises are easily affected by financial problems in the process of green transition. They should choose the most favorable mode according to the interest rate of different financing modes. 2) Enterprises should weigh the pros and cons of joining the blockchain platform, start with an accurate assessment of the bankruptcy risk of the borrower and promote the development of supply chain finance. 3) Joining the blockchain platform enables supplier to evaluate the credit information of manufacturer more accurately, which helps supplier and manufacturer choose more favorable financing modes.