Train timetable rescheduling (TTR) aims to promptly restore the original operation of trains after unexpected disturbances or disruptions. Currently, this work is still done manually by train dispatchers, which is challenging to maintain performance under various problem instances. To mitigate this issue, this study proposes a reinforcement learning-based approach to TTR, which makes the following contributions compared to existing work. First, we design a simple directed graph to represent the TTR problem, enabling the automatic extraction of informative states through graph neural networks. Second, we reformulate the construction process of TTR's solution, not only decoupling the decision model from the problem size but also ensuring the generated scheme's feasibility. Third, we design a learning curriculum for our model to handle the scenarios with different levels of delay. Finally, a simple local search method is proposed to assist the learned decision model, which can significantly improve solution quality with little additional computation cost, further enhancing the practical value of our method. Extensive experimental results demonstrate the effectiveness of our method. The learned decision model can achieve better performance for various problems with varying degrees of train delay and different scales when compared to handcrafted rules and state-of-the-art solvers.