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This paper proposes a scheme for constructing an Internet Protocol (IP) version 6 over low-power wireless personal area networks (6LoWPAN) wireless sensor network based on a cluster tree. In the cluster generation algorithm, a cluster tree is always an isolated node with the maximum number of neighbor isolated nodes that launches the cluster generation process; therefore, the total number of cluster heads is minimized. In the cluster-tree construction algorithm, the cluster-tree architecture is proposed, and the cluster-tree construction algorithm minimizes the total number of nodes included in a cluster tree; therefore, the routing cost is reduced. In the cluster-tree repair algorithm, when a cluster head or a cluster associate node fails or moves, a new cluster head or cluster associate node is elected to maintain the cluster-tree topology. This paper compares the performance parameters of Least Cluster Change algorithm with Lowest-ID, Root-based Lowest-ID cluster constructing mechanism, and the proposed scheme, including the cluster-tree topology stability, the routing memory cost, and the routing update cost. The analytical data show that the performance of the proposed scheme is better.