A two-stage decomposition approach based on a novel multi-agent system (MAS) is proposed for the distributed resource constrained multi-project scheduling problem (DRCMPSP). In stage one, from the point of view of each local project manager, a forward-backward hybrid genetic algorithm (FBHGA) is developed to generate an initial local schedule with the objective of minimizing individual project makespan. In stage two, from the global perspective of project management office, a sequential game-based negotiation mechanism is employed to eliminate global resource conflicts with the objective of minimizing total tardiness cost (TTC). The proposed approach is tested on 140 benchmark problem instances. According to the computational results, high-quality local project schedules can be obtained by FBHGA in stage one. Furthermore, it is observed that our method is capable of dealing with various complex multi-project instances under different degrees of resource conflicts in reasonable CPU running time. Compared to the existing decentralized methods for DRCMPSP, the proposed approach with sequential game-based negotiation mechanism shows the superiority in producing multi-project schedules with lower TTC, especially for large-size and strong conflicting instances.