Carbon emission reduction has become a common hot topic around the world. Although the previous literature has proven that the asymmetric information and fairness concerns would influence the operational strategy for low-carbon supply chain, it hardly touched the asymmetric information of fairness concerns, which contradicted practical observations and experimental evidence. Incorporating the asymmetric information of fairness concerns, this paper investigates a low-carbon supply chain consisting of a manufacturer and a retailer with discrete types including selfish S-type and fairness-concerned F-type. The manufacturer can observe and thereby know the behavioral type of the retailer in the scenario of symmetric information, while it cannot in the scenario of asymmetric information. In the approach of game theory, the optimal carbon emission reducing strategy and pricing strategy in the symmetric scenario and asymmetric scenario are achieved successively. By comparing the above two scenarios, the impacts stemming from the asymmetric information of fairness concerns at the individual level and systematic level are analyzed, respectively. A case study is offered before concluding some implications for the supply chain management. The findings include the following: Firstly, the asymmetric information of fairness concerns enhances the carbon emission reduction significantly. Although the fairness concerns alone decrease the carbon emission reduction, the asymmetric information increases with the dominating power. Secondly, the asymmetric information of fairness concerns raises the wholesale price and retail price dramatically. Although the impact of either fairness concerns or asymmetric information randomly changes with the behavioral type and information structure, their interactive impacts are stable and change smoothly. Thirdly, the asymmetric information of fairness concerns promotes a fairer profit distribution, while either fairness concerns or asymmetric information alone hardly changes the overall profit of the low-carbon supply chain.