In this paper, we address the time-of-arrival (TOA) based localization problem in an adverse environment, where line-of-sight (LOS) signal propagation between the source and the sensor is not readily available, in which case we have to resort to non-line-of-sight (NLOS) signals. Two convex relaxation methods, i.e., the semidefinite relaxation (SDR) and the second-order cone relaxation (SOCR) methods, are proposed to mitigate the effect of NLOS errors on the localization performance. We consider two separate cases in which the information of the NLOS status is totally unknown and perfectly known, respectively. The proposed methods can be applied without knowing the distribution of NLOS errors. Moreover, we propose a NLOS error mitigation method that is robust to detection errors, which are generated in the process of detecting NLOS paths. Simulation results show that the proposed convex relaxation methods outperform some existing state-of-the-art methods.