By noting the problem such as low energy efficiency and unreliable communication links in existing studies on wireless sensor networks(WSNs), a novel topology control algorithm based on the optimally rigid graph theory is proposed. A function, which can comprehensively reflect both link quality and energy consumption, is built to weight communication links with strong reliability and high efficient utilization of energy in the proposed algorithm. It is proved that the proposed algorithm has the properties of low average node degrees and good link performance. Finally, some simulation results show that the energy consumption can be reduced efficiently and network life can be prolonged by using the proposed algorithms, compared with the existing topology control algorithms.