The network lifetime is limited by key nodes in wireless sensor networks (WSNs). These nodes around the base station undertake a heavy load and die earlier than the others, so an energy hole emerges. In this study, an energy-balanced strategy that contributes to redistributing energy consumption of the network is proposed for WSNs through the innovative use of complex networks synchronization theory. The betweenness centrality in complex networks is used to measure the importance of the node in the network. Constructing energy consumption synchronization functions and decreasing the maximum betweenness of the node in this study improves the synchronization capacity of energy consumption and weakens the effect of key nodes on the performance of the network, the effect of key edges is also investigated in this study. Experiment results show that compared with other algorithms, the proposed strategy delays the appearance of the first death node, therefore prolongs the lifetime of the network effectively and helps achieve balance in the energy consumption of nodes.