A loyalty program is a type of incentive to reward customers' perceived value and enhance their purchasing behavior. The key to the success of a loyalty program is to allow customers to more actively participate in the program. One possible solution is to allow customers to sell out idle loyalty points and buy in the points that they need. On the basis of a call auction, this study designs a peer-to-peer exchange mechanism for customers to realize the above trade. In addition, a blockchain-based system is developed to support the issuance, redemption, and exchange of loyalty points. In this study, Hyperledger Fabric is adopted as the underlying blockchain technology because it has some features that are beneficial to a cross-organizational coalition loyalty program. This study also proposes a feasible multi-host deployment scheme for the Hyperledger Fabric blockchain network that is suitable for our application scenario. Finally, some implementation results are given to demonstrate the system process from the perspective of the application layer. The mechanism proposed in this study is helpful to improve the likelihood of successfully exchanging points, thus accelerating the circulation and use of loyalty points.