Abstract: To solve the problems in the sensitivity and rapidity of the flexible DC lines protection, starting from the perspective of the time domain waveform differences of the fault traveling waves (TW), this paper makes a mathematical analysis of the waveform characteristics of the fault reverse TW after the faults of the flexible DC power grid lines, and obtains the difference between the time domain expressions of the fault voltage reverse TW under the internal and external faults. In order to extract the characteristic difference between the fault TW waveforms inside and outside the area, the Levenberg-Marquardt method is used for data fitting according to the fitting function corresponding to the external faults. Then, a non-unit TW protection for the flexible DC lines based on the fitting residual size of the fault voltage inverse TW is proposed. Finally, the simulation based on the PSCAD/EMTDC shows that the scheme is able to identify all the faults of the DC lines quickly and correctly within the data window of 1 ms /20 kHz with high rapidity, sensitivity and reliability, and that it has strong robustness against the noise interference and small current limiting reactor value.