Due to the increased popularity of group-oriented applications and protocols, group communication occurs from network layer multicasting to application layer telephonic and video conferencing. In this scenario, security services are necessary to provide authenticity, integrity and communication privacy. Even though one-to-one communication is well established with good standard and security, still the group communication remains unexplored, since the group communication is not as simple as the one-to-one communication extension. In group Diffie–Hellman (GDH) key agreement protocol, all the group members combined to generate a group key, since many GDH key agreement protocols utilize the original Diffie–Hellman (DH) key agreement protocol to arrange all the group members in a logical ring or a binary tree to exchange DH public key. From these, there are two significant aspects which influence the efficiency of the GDH when the member of the groups gets increased. Here, we propose GDH key agreement protocol constructed on secret key sharing and forward secrecy with single-mode key confirmation and digital certificate of the DH public key to afford authentication of group keys. By using this algorithm, messages and key updates will be restricted to the group; hence, the computation load is distributed among the user equipment. BAN logic analysis and the experimental results show that our proposed protocol performs better for the key establishment in terms of computational cost and memory.