Dynamic contingency analysis (DCA) for modern power systems is fundamental to help researchers and operators look ahead of potential issues, arrange operational plans, and improve system stabilities. However, since the system size and the number of contingency scenarios continue to increase, pursuing more effective computational performance faces many difficulties, such as slow algorithms and limited computing resources. This research accelerates the intensive computations of massive DCAs by implementing a two-level hierarchical computing architecture on graphical processing units (GPUs). The performance of the designed method is examined using four test systems of different sizes and compared with a CPU-based parallel approach. The results show up to 2.8x speedup using one GPU and 4.2x speedup using two GPUs, respectively. More accelerations can be observed once more GPUs are configured. It demonstrates that the proposed architecture can significantly enhance the overall computational performance of massive DCAs while maintaining a strong scaling capability under various resource configurations.