In order to improve the ability of the modular multi-level converter to quickly clear and isolate faults in the multi-terminal flexible DC grid, this paper analyzes the characteristics of current faults in the multi-terminal flexible direct current grid, introduces the comprehensive distance of current fault waveform, and proposes a line protection method based on the similarity of current fault waveform. This protection method firstly uses Euclid DTW (Dynamic Time Warping) distance and entropy weight method to process electrical quantity signals, calculates the comprehensive distance of current fault waveform of two converter stations, and builds the protection criterion based on the similarity of current fault waveform. Then, the fault identification is realized by using the calculated comprehensive distance, and the fault pole identification is realized by using the ratio of comprehensive distance between positive and negative poles. Finally, PSCAD was used to build a simulation model to output the fault data under different fault conditions, and MATLAB was used to process the fault data to verify the protection algorithm. The simulation results show that the proposed method has good resistance to high resistance, and its rapidity and adaptability are further improved. The research results will provide a theoretical basis for the safe and reliable operation of flexible DC power grid.