The long-term exposure of submarine cables to the complex marine environment is likely to create a low impedance fault, leading to the breakdown of power system in the seafloor observation network. Therefore, fault location of submarine cables is the key basis for long-term and continuous observation of the ocean in the submarine observation network, which is critical to reduce the maintenance cost of submarine cables and improve the reliability of power transmission in the submarine observation network. In this paper, the transient current travelling wave generated when there is a low impedance fault is used to locate the fault point of the submarine cable in the seafloor observation network. Firstly, the low voltage pulse reflection method is applied to measure the propagation velocity of transient current travelling wave. Secondly, adaptive variational mode decomposition combined with Teager energy operator is employed to extract the fault time of transient current travelling wave. Finally, the fault point of submarine cable is located according to the propagation velocity and fault time of transient current travelling wave. The experimental results show that the research can quickly and effectively locate fault points of submarine cables and has good application value in the seafloor observation network.