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Sink mobility has attracted much research interest in recent years because it can improve network performance such as energy efficiency and throughput. An energy-unconscious moving strategy is potentially harmful to the balance of the energy consumption among sensor nodes so as to aggravate the hotspot problem of sensor networks. In this paper, an autonomous moving strategy for the mobile sinks in data-gathering applications is proposed. In the solution, a mobile sink approaches the nodes with high residual energy to force them to forward data for other nodes and tries to avoid passing by the nodes with low energy. Simulation experiments are performed to compare the solution with other three data-gathering schemes. The simulation results show that this strategy cannot only extend network lifetime notably but also provides scalability and topology adaptability.