Railway disturbances occur every day and train rescheduling is conducted by human experts. Approaches for automating rescheduling have been widely studied (e.g., heuristic approach and mixed integer problem-based approach). However, extant research is still inadequate for employing the approach in practical application in terms of size, run-time, and solution accuracy. In this research, we simulate train dispatching using graph theory and propose a reinforcement learning method (i.e., Deep Q-Network (DQN)) for rescheduling. We also show experimental results of this algorithm. DQN presented positive results for over 50% of test cases, and its train rescheduling decreased approximately 20% of passengers' dissatisfaction in a certain case. It can be expected that applying a DQN approach to real-world scale cases by will improve methods to handle larger-scale networks.