At present, it is still difficult to realize arc-extinguishing of large DC currents for DC breakers. A converter with fault self-cleaning capability can cut off the fault current quickly without DC breakers, which provides a new direction for research on protection of flexible DC grids. This article proposes a protection scheme for flexible DC distribution grids based on a full-bridge modular multilevel converter (MMC). The discrete wavelet transform is used to extract the maximum modulus of the fault current traveling wave. The fault can be determined by comparing the polarities of the maximum modulus of the fault current waveform obtained at the two ends of the DC line. A startup criterion is designed to avoid the interference of an out-of-zone fault, which increases the reliability of protection. The simulation results in PSCAD/EMTDC verify the proposed protection scheme, which can be adopted in flexible DC distribution grids.