When a single-phase grounding fault occurs in a power distribution system, the fault characteristics are not prominent and are easily drowned out by noise, making fault line selection difficult. A fault line selection method based on improved empirical wavelet transform (EWT) and GIN network is proposed to solve this problem. Firstly, EWT is optimized using kurtosis as the basis and N-point search method. EWT decomposes the electrical signal into a series of modal components, and noise is filtered out by weighted permutation entropy to reconstruct the signal, obtaining a denoised electrical signal. Then, according to the topology of the power distribution network, a corresponding graph structure is constructed. The Mahalanobis distance between each point and the overall structure in the denoised electrical signal is calculated and used as the input to each node in the GIN network. Finally, the GIN network autonomously mines the characteristics of each graph structure, performs graph classification, and realizes fault line selection. Experimental results show that the proposed method has a solid anti-noise ability and an accuracy of up to 99.95%, effectively completing fault line selection in power distribution networks.