Sensor node localization is an important issue in wireless sensor networks (WSNs) due to the dynamic nature of sensor deployment. Generally, in wireless sensor network localization, the absolute positions of certain anchor nodes are required based on the use of global positioning systems, then all the other nodes are approximately localized using various algorithms based on a coordinate system of the anchors. This paper proposes a neighbor position-based localization algorithm (NPLA) that can greatly enhance the positioning accuracy when compared with current overlapping connectivity localization algorithms that attempt to use the observation of connectivity to a set of anchors to determine a node's position. The proposed method localizes the sensor nodes using both the anchors' positions and neighbor node information. However, unlike existing overlapping-based methods, the proposed NPLA does not assume the same radio transmission range. A simulation study is used to demonstrate the positioning accuracy of the proposed method with different anchor and sensor node densities.