Aiming at the influence of distributed capacitance on differential current in long HVDC transmission lines, the waveform characteristics of differential current and distributed capacitance current is investigated. It is discovered that the waveforms similarity between differential current and distributed capacitance current can effectively identify internal fault and external fault. On this basis, normalized Euclidean distance is adopted to extract the similarity features, and then a new principle of pilot protection for hybrid multi-terminal HVDC transmission lines based on Euclidean distance is proposed. Finally, extensive simulation tests on three-terminal bipolar Hybrid-MTDC transmission system built in PSCAD/ EMTDC show that the proposed protection can detect faults rapidly and accurately, does not depend on complicated calculation, strict data synchronization and precise line parameters, with high sensitivity and reliability.