Accurate fault location for underground cables in MMC-HVDC grids reduces the time finding faults as well as the system operational costs. For MMC-HVDC grids, the data window during faults is usually short. During such severe transients, the frequency dependent line parameters of the underground cables have strong influence on the fault location accuracy. In this paper, a novel fault location algorithm for underground cables in MMC-HVDC grids is proposed. First, a multi-layer model for the underground cable using partial differential equations is proposed, which considers the distributed and frequency dependent line parameters in time domain. Afterwards, the numerical finite difference solution of the multi-layer model is proposed to obtain the voltage distributions along the entire cable. Finally, the voltage method is applied to locate faults. Numerical experiments show that the multi-layer model accurately considers the frequency dependency of the cable parameters, and the solution of the model obtains accurate voltage distribution even during system transient. Extensive test cases prove that the proposed algorithm locates faults with less errors than the existing algorithm. The method is also compatible with a relatively low sampling rate (20 kHz) and a short data window (5 ms).