The existing physical entity boundary consisted by smoothing reactor and DC filters makes high frequency component attenuated strongly through simulating and analyzing the internal and external fault voltage of high-voltage direct current（HVDC） transmission lines. The aerial mode voltage of two terminals of the line is smooth in short time window when external fault occurs， which makes its fractal dimension equal to one; while for internal faults， the fractal dimension is larger than one， because the transient voltage contains more high frequency components. The internal and external faults identification algorithm based on fractal dimension of the single-ended is proposed. The proposed method is proven effective and reliable through massive PSCAD simulations. The reason of proposed method having high fault resistance tolerance is analyzed by discussing waveform features on condition of various fault resistance and the mechanism of box dimension computation.