There is a problem in that the characteristics of weak fault signals are not obvious when there is interference on the distribution network. This makes it difficult for traveling wave acquisition equipment to effectively detect the fault traveling wave signals. Thus a method of fault traveling wave detection based on signal spectral characteristics is proposed. By analyzing the transmission characteristics and frequency characteristics of the fault traveling wave in distribution networks, a start-up criterion is established based on the waveform incremental ratio. It can preprocess the sampling data of the equipment, and reduce the false start-up of the traveling wave equipment. Then, the robust local mean decomposition (RLMD) method is used to process the sampling data, filter out the interference signal during the sampling process, and reduce the influence of the noise signal. Finally, given that it is a characteristic of the traveling wave that the low-frequency content attenuates less but the high-frequency content attenuates faster, an identification criterion is established to identify the fault traveling wave signals. Simulations show that the proposed method can effectively detect the fault traveling wave signals during weak faults.