Recently, positioning services have received considerable attention. The primary source of the positioning error is non-line-of-sight (NLOS) propagation. To address this problem, we propose a novel NLOS mitigation scheme, in which the geometric relationship between a base station and a mobile station is used. This makes it possible to identify range measurements corrupted by NLOS errors, and the mobile station can then estimate its position through line-of-sight (LOS) measurements. Moreover, the threshold of the NLOS detector is derived via a hybrid method using both the analytical derivation and computer simulation, which significantly reduces the difficulty of identifying thresholds. After identifying the NLOS measurements, a two-step weighted-least-squares algorithm is used to obtain the localization, in which both range and angle measurements are considered. The simulation results reveal that the proposed algorithm yields a high identification probability of NLOS measurements, which results in improved localization performance.