In this paper, the authors discuss about the Group Key (GK) which is shared only by a group of mobile devices. This paper explains a new group key management framework for the environment with dynamic mobile subscribers. Group key management plays very efficient and necessary role in mobile communication for enabling access control. The big thing is how to minimize the communication cost for generating rekeying among group members. Previously, the concept is based on the assumptions where the group members have the same leaving probabilities and also that the tree is balanced and complete, but these assumptions are impractical.