In Internet, IP multicast has been used successfully to provide an efficient, best-effort delivery service for group communication applications. However, applications such as multiparty private conference, distribution of stock market information, pay per view and other subscriber services may require secure multicast to protect integrity and confidentiality of the group traffic, and validate message authenticity. Providing secure multicast for group communication is problematic without a robust group key management. In this paper, we propose a group key management scheme based on the secret sharing technology to require each member by itself to generate the group key when receiving a rekeying message multicast by the group key distributor. The proposed scheme enforces mutual authentication between a member and the group key distributor while executing the rekeying process, and provides forward secrecy and backward secrecy properties, and resists replay attack, impersonating attack, group key disclosing attack and malicious insider attack.