Many enterprise networks require flexible dynamic group communications on the Internet. When we develop these systems on multicast communication framework, various types of security threats will occur. As a result, construction of secure group communication that protects users from intrusion and eavesdropping are very important matters.In this paper, we propose an efficient key distribution method for a secure group communication over multicast communication framework. In this method, we use IP multicast mechanism to shorten re-keying time to minimize adverse effect on communication. In addition, we introduce a proxy mechanism for replies from group members to the group manager to reduce traffic generated by re-keying.We define a multicast communication network model and evaluate the proposed method by computations using the model. From results of the evaluation, the proposed method will shorten the re-keying time and reduce concentration of traffic to the group management server in large systems.