Currently, most traveling wave protection of flexible DC power grids only considers short-circuit faults when configured. When breakage faults occur, the correctness of protection actions is unclear. In response to this problem, the action characteristics of traditional traveling wave protection under breakage faults are first analyzed. It is concluded that traditional traveling wave protection cannot correctly identify short-circuit and breakage faults. Thus, the second current traveling wave front characteristics and line voltage characteristics at the receiving end of the line under breakage and short-circuit faults are explored. The first current traveling wave characteristics at the sending end of the line and the characteristics of the product of voltage and current changes at both ends under the two kinds of faults are studied. A traveling wave protection scheme considering both short-circuit and breakage fault identification is proposed. The performance of the proposed protection scheme is verified on the PSCAD/EMTDC simulation platform. The results show that the protection scheme can accurately recognize and cope with faults of various conditions and has high speed and resistance to noise interference.