Many emerging mobile wireless applications depend upon secure group communication, in which a secure and efficient group rekeying algorithm is very important. In this paper, a rekeying algorithm named DGR (distributed group rekeying algorithm) is proposed, which is based on DGKMF (distributed group key management framework). DGR algorithm generates a group key with local secrete information, and is suitable for mobile ad hoc networks. In order to further reduce the communication complexity, the DGR algorithm is improved on by generating a cluster dynamically in the rekeying process, and the CDGR (cluster distributed group rekeying algorithm) is proposed. The security, correctness, and completeness of the two algorithms are discussed in this paper, and their message complexity costs are evaluated. Simulation results demonstrate that the two algorithms are better than other algorithms and protocols such as CKD, GDH v.2 and BD in the group rekeying success ratio and delay, and the CDGR is better than GDR in the group rekeying delay because it uses the cluster in the rekeying process.