With the increasing popularity of Internet and e-commerce, manufacturers have chosen to produce and sell green food through a dual-channel supply chain (DCSC). However, manufacturer and retailer's attentions on profit distribution and fairness of the DCSC have become the major concern. Therefore, how to determine the equilibrium prices and how the greenness level and fairness concern affects the decisions of DCSC members are the most important issues to be solved. In this study, three scenarios are inspected: all DCSC members are neutral; the manufacturer has fairness concern; the retailer has fairness concern. Numerical studies illustrate that when manufacturer raises fairness concern, the profits of DCSC members will decrease; when the retailer raises fairness concern, the profit of the manufacturer will decrease, while the profit of the retailer and the DCSC will increase. However, the influence of the fairness concern on DCSC will decrease when it rises to a certain extent.