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In this paper, we propose a cluster-based group key management scheme for wireless sensor networks(WSNs) that targets at reduce the communication overhead and storage cost of sensor nodes. In the proposed scheme, a group key is generated by the collaboration of cluster head and nodes within the cluster. Only cluster heads take responsible for reconstruct and delivery the group key. Performance evaluations demonstrate that the proposed scheme maintains a good level of security while significantly reduced the communication overhead compared with the existing schemes, especially in a large scale WSN.