Uncertainty on the fault traveling wave velocity, the difficulty of wave head extraction, the randomness of noise interference and other factors in DC lines restrict the application of fault location technology in a DC power grid. To reduce the influence of the above factors on positioning accuracy, a fault location method based on characteristic rational spline LMD (CRS-LMD) and singular value decomposition (SVD) is proposed. First, the optimal pole coefficient is selected with the use of the feature scale, and tightness of the fitting curve is adjusted by rational spline interpolation. The local mean decomposition of the fault voltage traveling wave is realized. Secondly, SVD is used to extract the fault travelling wave head accurately. Finally, a simulation model of the Zhangbei ±500 kV flexible DC power grid is built in PSCAD/EMTDC to simulate various fault situations and output fault data. Matlab is used to process the fault data and verify the positioning algorithm. The results show that the proposed algorithm can realize fault location with different fault distances and fault types, and guarantee high accuracy under when there is superimposed noise and transition resistance.