Most of the group key management schemes proposed in traditional networks rely on a reliable node. Different from the traditional networks, sensor networks don't have such reliable nodes and their resources are constrained. So all these schemes can't be used in sensor networks directly. Proposed in this paper is a group key management scheme based on the distributed rekeying authority. And a broadcast mechanism is introduced in the process of group rekeying. Furthermore, three novel polynomials are presented to revoke compromised nodes and distinguish rekeying information's integrality. Extensive analyses and simulations show that the proposed scheme can provide a high level of security, reduce communication and storage overheads, and avoid the problem of isolated nodes.