Aiming at the problems currently existing in transmission line protection for modular multilevel converter (MMC) based high voltage direct current (HVDC) grids, this paper proposes an improved single-ended fault detection scheme for MMC-HVDC transmission lines. The proposed scheme is based on the frequency-domain attenuation rate of the initial voltage traveling wave (IVTW). Firstly, the values of the IVTWs generated by the internal and external faults are calculated respectively based on the equivalent model of the four-terminal MMC-HVDC grid. Due to the boundary effect of DC inductors installed on both ends of DC lines, the attenuation rates of IVTWs with the increase of the frequency under internal and external faults have different characteristics. The detail coefficients of the IVTW in different frequency bands are extracted by stationary wavelet transform at different scales, and the amplitudes of the IVTW in different frequency bands are quantified by wavelet transform modulus maximums (WTMMs) at corresponding scales. A criterion for identifying internal and external faults is constructed based on the square of the frequency-domain equivalent attenuation rate of the IVTW. Lastly, simulation results under diverse fault conditions verify the effectiveness of the proposed fault detection scheme.