Enterprises adopting a circular economy approach can effectively solve the severe situation of resources and the environment, and recycling is considered an effective means to solve environmental issues. Simultaneously, blockchain technology (BT) has been used to enhance product quality trust. However, there is limited literature on how to choose between monopolistic and competitive recycling modes by considering BT. This paper uses a game involving a manufacturer, a retailer, and a third-party recycler (TPR) in a closed-loop supply chain (CLSC). The retailer can recycle on itself and compete with the TPR for recycling used products. The results show that BT adoption could increase the recycling rate and demand for remanufactured products. BT benefits the firms in the CLSC when they control usage costs, regardless of whether competitive recycling mode is used or not. In addition, whether BT is adopted or not, CLSC firms prefer competitive recycling mode only when the competitive intensity exceeds a specific threshold. Moreover, choosing an appropriate recycling mode can alleviate the negative impact of BT on the environment, then an all-win result can be obtained for CLSC firms, consumers, and society. These results can give suggestions for managers to optimize their supply chains regarding adopting BT and implementing recycling mode. In the future, we can expand our research on the transfer price of used products, the positive and negative effects of BT, and BT cost-sharing strategies.