In this study, we present a novel mobile anchor-assisted node Localization algorithm using Intersection and Exclusion (LIE) for wireless sensor networks. It sets up a discrete network model and then solves a system of geographic constraints based on connectivity information from the underlying communication network. Moreover, after the nearby nodes have completed localization, they become beacons, then cooperate with each other to localize the left unknown nodes in an incremental way and lastly obtains the optimum trajectory of mobile anchors and all the nodes locations. Simulation results demonstrate that the proposed LIE algorithm can improve significantly the localization accuracy compared to other similar positioning technology.