This paper proposes a robust faulted line-section location method based on the normalized quantile Hausdorff distance (NQHD) algorithm for detecting single-phase-to-ground faults in distribution networks. The faulted line section is determined according to the characteristic differences between the zero-sequence currents on the faulted and healthy line sections. Specifically, the zero-sequence currents at both ends of a healthy line section are highly similar to each other, while such is generally not the case on a faulted line section. The NQHD algorithm can disregard extremes or outliers while also providing a normalized scaling in different scenarios. Thus, it can be applied to calculate the robust waveform similarity of zero-sequence current waveforms at both ends of different line sections for identifying reliably the faulted line section even under the interference of outliers. The results demonstrate the good performance of the proposed method in detecting single-phase-to-ground faults under different fault conditions. Comparative tests with the existing methods confirm the advantageous robustness of the proposed method against the impacts of outliers and noises.