The natural fractures, e.g., the bedding-parallel fractures (BPF), have a significant impact on the storage space and horizontal permeability of continental shale oil reservoirs. However, the conventional logging response of BPF is complex. To solve the problem of BPF density prediction, we propose the Edge Generation Weighted Graph Convolutional Network (EG-WGCN) method, which is an improved Graph Convolutional Network (GCN). The new method integrates the relationship information between the fractures and lithology into the edge generation method, and adds the generated edge weight information into the message passing process, thereby effectively improving the accuracy of fracture density prediction. The prediction process is divided into three steps: first, using conventional logging sampling points as vertices, establish vertex sets for each lithology and single lithologic layer. Second, based on the depth sequence of a single lithologic layer and the Euclidean distance of the same lithologic vertex sets, the connection between vertices is established and overlapping edges generated by the above methods are given higher weights. Third, the vertices in the constructed graph are classified through graph convolutional layers, which are integrated into the edge weight information. This method is applied to the fracture density prediction of continental shale oil reservoirs in the Mahu Sag of the Junggar Basin, western China. The results show that the accuracy of our proposed EG-WGCN method in testing data is 95.13%. Compared to the GCN (boundless) without using the edge generation method and EG-GCN with the edge generation method but without the weighted aggregation mechanism, model accuracy is improved by 14.48% and 1.22%, respectively. In summary, this method proves that if a proper ML model is used, conventional logging data can become valuable for predicting BPF density with high accuracy even when cores are missing.