With the rapid development of information and communication technology, the wireless sensor network (WSN) has shown broad application prospects in a growing number of fields. The non-line-of-sight (NLOS) problem is the main challenge to WSN localization, which seriously reduces the positioning accuracy. In this paper, a robust localization algorithm based on NLOS identification and classification filtering for WSN is proposed to solve this problem. It is difficult to use a single filter to filter out NLOS noise in all cases since NLOS cases are extremely complicated in real scenarios. Therefore, in order to improve the robustness, we first propose a NLOS identification strategy to detect the severity of NLOS, and then NLOS situations are divided into two categories according to the severity: mild NLOS and severe NLOS. Secondly, classification filtering is performed to obtain respective position estimates. An extended Kalman filter is applied to filter line-of-sight (LOS) noise. For mild NLOS, the large outliers are clipped by the redescending score function in the robust extended Kalman filter, yielding superior performance. For severe NLOS, a severe NLOS mitigation algorithm based on LOS reconstruction is proposed, in which the average value of NLOS error is estimated and the measurements are reconstructed and corrected for subsequent positioning. Finally, an interactive multiple model algorithm is employed to obtain the final positioning result by weighting the position estimation of LOS and NLOS. Simulation and experimental results show that the proposed algorithm can effectively suppress NLOS error and obtain higher positioning accuracy when compared with existing algorithms.