In the secure group communication, data is transmitted in such a way that only the group members are able to receive the messages. The main problem in the solution using symmetric key is heavy re-keying cost. To reduce re-keying cost tree based architecture is used. But it requires extra overhead to balance the key- tree in order to achieve logarithmic re-keying cost. The main challenging issue in dynamic and secure multimedia multicast communication is to design a centralized group key management scheme with minimal computational, communicational and storages complexities without breaching security issues. Several authors have proposed different centralized group key management schemes, wherein one of them proposes reducing communicational complexity but increases computational and storage costs however another proposes decreasing the computational and storage costs which eventually breaches forward and backward secrecy. In this paper we propose a comparatively more efficient centralized group key management scheme that not only minimize the computational, communicational and storages complexities but also maintaining the security at the optimal level. The message encryptions and decryptions costs are also minimized. Further, we also provide an extended multicast scheme, in which the several requests towards leaving or joining the group can be done by large number of members simultaneously. In order to obtain better performance of multicast encryption, the symmetric-key and asymmetric-key cryptosystems may be combined.