The reduction in carbon emissions by industrial enterprises is an important means for promoting environmental protection and achieving sustainable development. To determine the impact of carbon emissions reduction on supply chain operation and financing decision-making, in this study we designed three financing strategies, i.e., bank loan financing, equity financing, and hybrid financing (a combination of bank loan financing and equity financing), for a manufacturer (leader) and a low-carbon supply chain composed of a capital-constrained retailer, constructed Stackelberg game models, solved the equilibrium results under each financing strategy using the reverse recursion method, and revealed the financing preference of the supply chain member companies through comparative analysis. The results showed that the increase in the consumers’ low-carbon preference and equity financing ratio have positive impacts on supply chain equilibrium, a result that is opposite that for the impact of the interest rate of bank loan financing; additionally, the abovementioned three factors jointly determine the profit of the manufacturer of the low-carbon supply chain, while the retailer’s profit is affected by the equity dividend ratio. Finally, we present the conditions for the financing preference of the manufacturer and the retailer. The findings of this study can provide references for low-carbon supply chain companies to make appropriate management decisions.