The Ganges River is the most important source as water resources for both Bangladesh and India, and this has resulted in many conflicts between these two countries. This conflict situation changed drastically in 1975 because India constructed the Farakka Barrage over the Ganges River near the border. India and Bangladesh had no discussions on this construction, and India acted it unilaterally. However, the countries made treaties about water utilization of the Ganges after construction, in 1975, 1977, and 1996. Sometimes the treaties were followed depending on the political situation of the two countries. The treaties are changed differently in some aspects. Nonetheless, the three treaties are generally advantageous to India which is situated of upstream the river. Bangladesh is more vulnerable to flood and drought than India because of the Farakka Barrage. From this aspect, flood and drought in Bangladesh might be said to be a man-made disaster. However, it is difficult for Bangladesh to offer a new effective option for dissolution of the conflict because Bangladesh is at a disadvantage economically and topographically to India. As for India, it is hard to think that India changes its preference internally. Therefore, the conflict between Bangladesh and India has been stagnant since they have only negotiated by themselves. In such a case, participation of a third party is thought as being able to improve the situation. In this study, Conflict Analysis is used for modeling and analyzing this conflict. It is based on game theory, and provides algorithms to calculate equilibria among decision makers who have different preferences. Based upon the framework of Conflict Analysis, the roles of a third party are classified and defined into three types: ‘Donor’, ‘Coordinator’, and ‘Arbiter’, which are jointly called ‘Complement’ on the whole. The graph model methodology is applied to the conflict between Bangladesh and India. First, the actual situation is modeled using Conflict Analysis. Second, the condition which is necessary to improve the current conflict is analyzed, and the role of a third party which realizes this condition is considered. Third, the role of ‘Coordinator’ is used to find what condition is needed to improve the outcome of the conflict. The intervention of a third party to the conflict is one of the measures taken practically toward settlement of conflict, but there are not so many third parties which recognize and declare what role they will play. For the case in which the third party intervenes in the conflict and where players have difficulty to achieve a settlement by themselves, a third party should be fair and equitable. To realize such a stance of a third party, proof of its role is considered as an essential procedure. Under this recognition, this study is thought to be able to provide a useful framework to define the process for conflict management.