This paper proposes a source localization solution ro-bust to measurement outliers in time differences of arrivals (TDOA) measurements. The solution uses a piecewise loss func-tion named as mixed Huber loss (MHL) proposed based on the classical Huber loss (HL) and its refined version. The MHL is able to effectively mitigate the impact of all levels of measurement outliers by setting two triggering thresholds. In practice, appro-priate triggering threshold values can be obtained through simu-lation given the level of measurement noise and a rough range of potential measurement outliers. A clustering based approach is proposed to further improve the robustness of localization solu-tion against reference sensor related outliers. Simulations are in-cluded to examine the solution \'s performance and compare it with several benchmarks. The proposed MHL based solution is shown to be superior to the classical solution and the bench-marks. The solution is shown to be even robust to multiple measurement outliers. Furthermore, the influence of range mea-surement outliers in the reference sensor can be effectively miti-gated by the clustering based approach.