Low-duty-cycle mechanisms can reduce the energy consumption in wireless sensor networks. Many related researches have been made in recent years. In the low-duty-cycle environment, the latency of sending packets from a sink to each node is much longer than traditional WSNs because nodes stay asleep most of the time. In this paper, the Centralized Cluster-based Location Finding (CCLF) algorithm is proposed to reduce the high latency in low-duty-cycle WSNs by finding a suitable position for the sink. The algorithm mainly consisted of three steps: (1) Cluster construction, (2) The fast look-up table (FLU-table) construction, and (3) Sink location decision. The simulation results show that the performance of the CCLF algorithm approaches the performance of the optimal algorithm. Moreover, the CCLF algorithm requires less operation time compared with the optimal algorithm.