When a single-phase ground fault occurs in a distribution network, the current is weak, the fault conditions are complex, and the performance of the existing fault detection techniques is unreliable. Thus this paper proposes a multivariate transient characteristic fault degree distribution network single-phase ground routing method using fundamental frequency shift. To retain the panoramic nature of transient features, the fundamental frequency component in the transient zero-sequence current is removed, and the Hilbert transform is used to calculate the transient zero-sequence current resolved signals. Then, a displacement factor is introduced to remove the fundamental frequency to retain all the transient features. Next, three typical transient feature metrics are calculated. Finally, a Copula is used to compute the joint distribution density function of the transient feature random variables and to calculate the fault degree of lines, and select the feeder with the largest fault degree as the faulty feeder. The effectiveness of the proposed methodology is verified by setting up a radial distribution network sample model, the arc fault model, and the IEEE 34-bus test system for the wind turbine and photovoltaic models in different fault conditions.