Whenever there is a disruption in areas with a high frequency of train operations, the delays of trains propagate and train passengers have to suffer inconvenience. A rescheduling of the train operations is then conducted by train dispatchers to revert to the original operational plan. The task is quite difficult and a severe burden for the dispatchers because of a variety of options for reverting to the original plan, the necessity for a swift action, and the absence of a proper evaluation criterion. Consequently, a computer-aided rescheduling-support system is required. In this paper, we present a mathematical programming approach for train rescheduling, focusing on minimizing the passengers' arrival delay at their destinations. We simultaneously model the train operations and passenger flow on the basis of mixed integer programming (MIP), and we obtain an optimal rescheduling plan in reasonable time in the case of a small disruption.