A Kconnected cluster topology control algorithm is proposed in this paper. The main content of the algorithm is the selection of the backbone nodes and the redundant backbone nodes during the procedure of the cluster forming and sleeping scheduling of the cluster nodes. In the selection of the backbone nodes, energy balancing, channel quality, node faults and mobility are taken into account. The sleeping scheduling gives different scheduling mechanisms for different types of nodes. The simulation results show that the algorithm has a good performance in network topology stability and lifetime with some fault tolerance.