In recent years, environmental protection has been paid more and more attention. Green credit policy (GCP) is one of the significant preferential policies for government to encourage enterprises to vigorously develop green projects. We are interested in the impact of the central bank’s GCP on the profits and optimal strategies of manufacturers and suppliers related to POF (purchase order financing). Specifically, we build a game-theoretical model consisting of a manufacturer, a bank and a green supplier and a non-green supplier. Furthermore, the optimal strategies of the manufacturer and suppliers when the bank or the government sets a carbon emission cap on suppliers are discussed. We come to some important conclusions about a GCP that promotes the development of green projects since it brings higher profits to both the manufacturer and suppliers than the lack of a GCP. Furthermore, the higher the production cost, the better the effect of a GCP. Under the carbon emission restrictions required by the government, the effect of GCP is weakened and the profits of the manufacturer and the suppliers are reduced to zero due to the gradually increasing delivery risks as production costs increase.