Recently, as the performance of mobile hosts rapidly improves and the bandwidth of wireless access networks grows up, the expectation for mobile multimedia communication services including many-to-many communications such as video-conferencing begins building. Mmulticasting is one of the key technologies to provide such services efficiently. The existing multicast protocol called Core Based Trees (CBT) is suitable for many-to-many communications in wired networks. In mobile networks, however, it has problems that the number of links of the multicast tree may increase and the end-to-end delay may not satisfy the QoS requirement from users due to tree reconstruction after handovers. Thus, we propose to change the core in consideration of the delay from the core to member nodes when a handover occurs and a new path is constructed. As a result, the proposed method decreases both the number of members who do not satisfy the delay constraint and the average number of total links of the multicast tree.