Tugboats are widely used near harbors to assist with various operations such as the berthing and deberthing of very large vessels and the towing of barges. Capsizing accidents involving tugboats occasionally take place when the tugboat makes rapid turns in harsh weather conditions. When there is little evidence suggesting how the accident occurred and when the crew members are missing, it is necessary to predict the time history of the towing vessel’s attitude and trajectory from its departure point to when and where it capsized, depending on various input parameters using a numerical simulation. In this paper, the dynamics of a tugboat and a towed barge in conjunction with the external force and moment were established, and the possible input parameters and operational scenarios which might influence the large roll motion of the tugboat were identified. As a result of analyzing the simulated time history of the excessive roll motion of the tugboat, it was found that roll motion can take place when the tugboat is situated on the crest of a wave and when it is pulled by a towed barge through a towing line. The main cause of the accident would be the parameters that primarily influence such situations. These are the wave parameters, course changing scenario, and the amount of tension.