The indoor localization algorithm with non-line-of-sight(NLOS) is studied. Firstly, we describe the techniques widely used in indoor localization and algorithms(dead reckoning, fingerprint identification, adjacent to detect, orientation of the pole, triangulation, multilateral, centroid localization), and summarize the principle, advantages, disadvantages and applicable scenario. Secondly, the necessity of studying NLOS identification and mitigation is illustrated by simulation test. Then, several algorithms of NLOS identification and mitigation are introduced respectively. NLOS identification algorithms include statistical methods, geometric relation methods, machine learning methods, channel feature extraction methods and virtual point density recognition methods. Moreover, NLOS mitigation algorithms include fuzzy theory methods, introduced equilibrium parameter methods, geometric relation methods, wavelet denoising methods, machine learning methods, convex optimization methods, residual methods, least square methods and multidimensional scaling methods. Finally, this paper summarizes the whole paper and points out the problems to be solved in NLOS indoor localization.