The rapid detection of direct current (DC) faults is one of the key technologies for the development of multi-terminal alternating current (AC)/DC hybrid distribution networks. The DC fault current rises quickly and affects the whole network. Therefore, DC faults must be detected much faster than AC faults. This paper proposes a fast DC fault detection method based on the voltage change rate of the current-limiting inductor (CLI) for the multi-terminal AC/DC hybrid distribution network. Firstly, the characteristics of the fault voltages and currents and of the CLIs are studied in detail, and the feasibility of using the voltage change rate of the CLI to detect DC fault is analyzed. Based on this, a primary fault detection method is proposed to identify the faulty line, determine the fault type and the fault poles using the amplitudes of the single-ended CLI voltage change rates. For high-resistance DC faults, a backup detection method using the directions and amplitudes of the voltage change rates of the double-ended CLIs is proposed. Finally, the proposed method is verified by MATLAB simulations. The simulation results show that the proposed method can detect all DC faults accurately, and the faulty line, fault type and fault poles can be determined quickly. The proposed method is not affected by the fault location, current-limiting inductance, power reversal of the converters, AC fault and communication delay.