Most of sensors in a wireless sensor network (WSN) are energy-limited. In order to prolong the network lifetime, some energy-efficient algorithms are proposed. Low Energy Adaptive Clustering Hierarchy with Deterministic Cluster-Head Selection (L-DCHS) is a well-known distributed clustering algorithm. In this paper, we propose a novel energy-efficient algorithm for wireless sensor networks (NEAW) based on L-DCHS. Our simulation shows that NEAW can prolong the network lifetime, and it is energy-efficient.