Flexible DC distribution networks based on a modular multilevel converter (MMC) have the advantage of no commutation failure. However, because of low inertia, weak damping and other characteristics of the converter, the fault current rises quickly and has a high peak, which is extremely harmful to the system. It is difficult to accurately select the fault feeder when a single-pole ground fault occurs in the DC distribution network. Thus a fault detection method for a DC distribution network based on the fluctuation characteristics of concavity and convexity (FCCC) of the inflection point dense area (IPDA) is proposed. First, a variational mode decomposition algorithm is used to decompose the zero-mode current of each feeder and select the feature components. Then, the second derivative of the feature component is calculated, the IPDA is selected, and the normalization process is carried out to obtain the FCCC of each feeder. Finally, the feeders that are different from the other feeders of the FCCC are determined to be faulty feeders. Simulation results show that the proposed method can quickly identify faulty feeders, and is less affected by factors such as transition resistance, sampling frequency, data window and noise.