Proposed a new topology-control algorithms which is based on k-connectivity. In wireless sensor networks, the existing topology-control algorithms now can not meet the needs of WSN in fault tolerance, connectivity, redundancy and so on. In LKETA, the node deletes redundant edges according to the information of local neighbor nodes, and it adjusts transmission power with the power adjustment algorithm to constitute a k-connected sub graph, then it can calculate the topology refresh cycle according to the rate of the neighbor nodes. This algorithm guarantees the connectivity, low the transmitted power of nodes, reduce the redundancy edges, and increase the channel capacity.