In this paper, we propose a new group key management scheme for wireless sensor networks in terms of the unreliable wireless channel and unsafe environment. Our proposed scheme implements node revocation through a broadcast polynomial to counteract the node compromise attack and inherits the idea of loss tolerance in LiSP to provide a reliable communication. The analysis shows that the proposed scheme can efficiently revoke the compromised sensor nodes, implicitly authenticate the updated group keys and tolerate the key-update message loss under the unreliable wireless communication channel.