When a grounding fault occurs in the distribution network with distributed generation, the network topology becomes intricate, making it challenging to extract fault characteristics, resulting in a decrease in the precision of fault discrimination. To address this issue, a graph isomorphism network (GIN) approach based on the parameterized adaptive graph learning (AdapGL) module is proposed, transforming the distribution network fault selection problem into a graph classification task. First, the adjacency matrix of the distribution network's topology graph is initialized. This matrix, combined with feature vectors from the robust local mean decomposition energy entropy and transient dielectric loss angle of line, will be input into the GIN. Then, the AdapGL module is integrated into the GIN, dynamically learning and updating the one‐way relationships between actual network nodes to complete the graph classification task. Finally, a radial distribution network model (RDNM) and an improved IEEE 34 nodes model are established, and the fault selection results of the AdapGL‐GIN method are compared with those of other methods. The results indicate that the proposed method achieves higher accuracy than other methods, demonstrating significant practical importance in engineering applications.