Remanufacturing has become a Frontier technology in sustainable manufacturing and enables end-of-life products to be restored to their new conditions. Although remanufacturing scheduling has been widely investigated, the relationship between remanufacturers and customers is rarely examined. Therefore, a new game-relationship-based remanufacturing scheduling model with sequence-dependent setup times is proposed herein. In the model, the relationship between the remanufacturer and customers is constructed as a non-cooperative game, and the interval due dates are set based on the uncertain product quality to achieve effective remanufacturing and improve customer satisfaction. Multiple remanufacturing lines differentiated based on the quality grade of products are integrated into the proposed model. In addition, sequence-dependent setup times are considered in the model, which depend on the similarity between two adjacent tasks processed on a reprocessing unit. An improved discrete particle swarm optimization algorithm is proposed to obtain Nash equilibrium solutions via an efficient global search structure and a local search strategy. The algorithm is embedded with the Nash equilibrium solution evaluation method and integrated with multiple genetic operators to update the particles. The performance of the proposed algorithm in solving the proposed model is verified via a comparison with three baseline algorithms for managing different problem instances.