Abstract: The traveling wave main protection is susceptible to the high-resistance faults, the current differential protection to the distributed capacitance, and there is a large time gap between the existing main and backup protection schemes. In order to solve the above problems and further improve the reliability of the protections, this paper proposes a new scheme of traveling wave longitudinal protection based on measuring the wave impedance Euclidean distance. By analyzing the difference between the amplitude and change trend of the measured wave impedance on both sides of the line during the internal and external faults of the flexible DC transmission lines, it is proposed to use dyadic wavelet transform to extract the wideband window to measure the wave impedance, and introduce the Euclidean distance and the similarity coefficient to express the amplitude and change trend of the wave impedance. Finally, the internal and external faults are distinguished according to the Euclidean distance and the similarity coefficient. The PSCAD simulation verifies that the protection principle can identify the internal and external faults reliably, sensitively and quickly, and it has a strong ability to withstand the transition resistance and noise interference.