Due to the serious problem of global warming, the ' low-carbon' concept has been accepted by more consumers. The vast majority of small and medium-sized supply enterprises in China don't have enough money to operate carbon reduction modification to satisfy consumers'need. In this paper, the 'max profit' model containing internal financing from the retailer to the supplier is built and solved by two-stage Stackelberg game in decentralized and centralized decisions. The research indicates that the increase of low carbon consumer preferences, internal and external financing interest-rate lead to higher gross profit in retailer-leading decentralized supply chain, and the unit cost of carbon emissions and external investment interest-rate will have negative effects on retailer-leading decentralized supply chain's gross profit, while the internal interest-rate is only related to wholesale price in supplier-leading decentralized supply chain. The centralized supply chain gross profit rises as the low carbon consumer preference increases and the unit cost of carbon emissions decreases. Meanwhile, the centralized supply chain gross profit remains invariable as the internal and external financing interest and external investment interest change. The conclusion of decentralized and centralized decision can be used in different types of supply chains in the actual low-carbon investment and financing.