Supply chain greening has become an important direction for sustainable development. This paper develops a two-stage game model involving a traditional manufacturer, a green manufacturer, and a retailer, to investigate the fairness concerns of the green manufacturer in a supply chain. Different from previous fairness concern models that focus on a single comparison relationship, this study incorporates both horizontal fairness concern with the competing traditional manufacturer and vertical fairness concern with the retailer into a unified framework for green supply chains. The results show that when traditional and green consumers hold equal market shares, the demand and profit of the green manufacturer are consistently higher than those of the traditional manufacturer, although this advantage diminishes as green R&D efficiency decreases. Moreover, increasing bidirectional fairness concern reduces the greenness of green products and significantly affects the retailer’s profit, while its impact on manufacturers’ profits is relatively limited. The effects of bidirectional fairness concern on product pricing depend on green R&D efficiency and the competitive relationship between green and traditional products. Based on these findings, managerial insights are provided for supply chain participants.