In this paper, we study the green credit financing equilibrium in a green supply chain (GSC) with government subsidy and supply uncertainty. The GSC system is composed of one manufacturer, two retailers, one bank, and the government. The manufacturer is subject to both supply uncertainty and limited capital. The manufacturer invests in the R&D of green products and borrows loans from the bank. The government subsidizes banks to encourage banks to provide loans to manufacturers with lower interest rates, which is termed “green credit financing”. The two retailers decide their order quantities with horizontal competition or horizontal cooperation. We first developed a Stackelberg model to investigate the green credit financing equilibriums (i.e., the interest rate of the bank, the manufacturer’s product green degree and wholesale price, and the retailers’ order quantity) under horizontal competition and horizontal cooperation, respectively. Subsequently, we analyzed how the subsidy interest rate, supply uncertainty, and supply correlation affect financing decisions regarding equilibrium green credit. We found that a high subsidy interest rate leads to a low interest rate of bank and the manufacturer can set a high level of green product and high wholesale price, while the retailers can set a high order quantity. Finally, we compared the green credit financing equilibriums under horizontal competition with those under horizontal cooperation using numerical and analytical methods. We found that, in general, the optimal decisions and profits of bank and SC members, consumer surplus, and social welfare under horizontal competition are higher than those under horizontal cooperation. The findings in this research could provide valuable insights for the management of capital-constrained GSCs with government subsidies and supply uncertainty in a competing market.