Abstract This study constructs a two‐level green supply chain (GSC) involving a manufacturer that makes greenness investments and a retailer that applies trade credit from the manufacturer. It is assumed that the manufacturer may open an online channel to form a dual‐channel GSC. Four models are considered based on whether the manufacturer opens the online channel and whether the retailer is fairness‐concerned. The equilibrium decisions and profits of GSC members are compared. The results show that regardless of whether the retailer is fairness‐concerned, the retailer prefers the dual‐channel GSC as long as the greenness level efficiency is high enough. Counterintuitively, a sufficiently low cost of opening an online channel does not always incentivize the manufacturer to open it, as additional conditions, such as a relatively high greenness level efficiency, are also required. Meanwhile, a higher fairness‐concerned degree may trigger the manufacturer to open the online channel.