The topology control strategies of wireless sensor networks are very important for reducing the energy consumption of sensor nodes and prolonging the life-span of networks. In this paper, we put forward a minimum-energy path-preserving topology control (MPTC) algorithm based on a concept of none k-redundant edges. MPTC not only resolves the problem of excessive energy consumption because of the unclosed region in small minimum-energy communication network (SMECN), but also preserves at least one minimum-energy path between every pair of nodes in a wireless sensor network. We also propose an energy-efficient reconfiguration protocol that maintains the minimum-energy path property in the case where the network topology changes dynamically. Finally, we demonstrate the performance improvements of our algorithm through simulation. The topology control strategies of wireless sensor networks are very important for reducing the energy consumption of sensor nodes and prolonging the life-span of networks. In this paper, we put forward a minimum-energy path-preserving topology control (MPTC) algorithm based on a concept of none k-redundant edges. MPTC not only resolves the problem of excessive energy consumption because of the unclosed region in small minimum-energy communication network (SMECN), but also preserves at least one minimum-energy path between every pair of nodes in a wireless sensor network. We also propose an energy-efficient reconfiguration protocol that maintains the minimum-energy path property in the case where the network topology changes dynamically. Finally, we demonstrate the performance improvements of our algorithm through simulation.