With the increasing popularity of Internet, e-commerce and environmental awareness, more and more manufacturers have chosen to produce and sell green food through a dual-channel supply chain (DCSC) to improve market and environmental performance, i.e., the demand, price, profit as well as greenness level. However, the implementation of online channels has triggered substantial changes in consumer behaviors, which arises fairness concern of the retailers and even manufacturers regarding price and profit distribution of the green food DCSC. Therefore, how to explore the influence of fairness concern on the interaction between the performance of green food DCSC and consumer behavior is a vital issue to be solved. To fill this research gap, this study constructs three models of fairness concern (all DCSC members are neutral; the manufacturer has fairness concern; the retailer has fairness concern) to analyze the effects of fairness concern coefficient on the performance of green food DCSC. The numerical studies show that, in general, the consumers' preference for green food will promote the greenness level of the product and thus heightens the total profit of DCSC. Changes in the market share of the offline will affect performance through fairness concern and transfer price. In particular, the results further illustrate that when the green food manufacturer raises fairness concern, the profit of DCSC members as well as the profit of the whole DCSC will decrease. Furthermore, when the green food retailer increases its fairness concern, the profit of the manufacturer will decrease, while the profit of the retailer and the profit of the whole DCSC will increase. However, it is worth noting that the influence of the fairness concern on the performance including pricing and profit of green food DCSC will be reduced when the behavior of fairness concern rises to a certain extent.