Flexible DC distribution networks have a strong capacity for new energy consumption and have received extensive attention from scholars in recent years, but fault location for DC distribution lines is a difficult task. To solve this problem, we propose using a comprehensive grey correlation degree analysis to analyze the similarity of aerial mode traveling differential current waveforms at the first and last ends of a DC line, thus achieving fault location by obtaining the optimal time shift. Additionally, we built a six-terminal flexible DC distribution network model in Matlab/Simulink for simulation and validation, showing that the method can complete the rapid and accurate location of all types of faults on a DC line, and that it possesses an anti-transition resistance capability, making it suitable and highly reliable for cases of low sampling frequency.