This paper studies optimal decisions in an authorized remanufacturing closed-loop supply chain (CLSC) consisting of a manufacturer, a retailer, and an authorized third-party remanufacturer with dual-fairness concerns (distributional fairness concerns and peer-induced fairness concerns). Four Stackelberg game models were developed: (i) the dual-fairness concerns are considered by a retailer (model F); (ii) the retailer does not consider both types of fairness concerns (model N); (iii) the retailer only considers the distributional fairness concerns (model D); (iv) the retailer only considers the peer-induced fairness concerns (model P). We use numerical analysis to examine the equilibrium outcomes under dual-fairness concerns. The results show that: (1) The increase in the coefficient of peer-induced fairness concerns will result in more profit for the manufacturer in most cases, while distributional fairness concerns always hurt the manufacturer; (2) In most parameter cases, the increase in the degree of distributional fairness concerns favors the retailer. The retailer considers only peer-induced fairness concerns when the degree of distributional fairness concerns is low and the degree of peer-induced fairness concerns is relatively high, whereas in other cases, two kinds of fairness concerns are ignored; (3) Model P is the most profitable and model D is most disadvantageous for the third party, however, for the manufacturer it is the opposite; (4) The impact of fairness concerns on the environment depends on the retailer’s attitude towards fairness concerns. Model P is better for the environment, while model D has the highest environmental impact. This study introduces dual-fairness concerns into the authorized remanufacturing CLSC model and provides theoretical references for authorized remanufacturing and sustainability practices.