Identifying the subtypes of low-grade glioma (LGG) can help prevent brain tumor progression and patient death. However, the complicated non-linear relationship and high dimensionality of 3D brain MRI limit the performance of machine learning methods. Therefore, it is important to develop a classification method that can overcome these limitations. This study proposes a self-attention similarity-guided graph convolutional network (SASG-GCN) that uses the constructed graphs to complete multi-classification (tumor-free (TF), WG, and TMG). In the pipeline of SASG-GCN, we use a convolutional deep belief network and a self-attention similarity-based method to construct the vertices and edges of the constructed graphs at 3D MRI level, respectively. The multi-classification experiment is performed in a two-layer GCN model. SASG-GCN is trained and evaluated on 402 3D MRI images which are produced from the TCGA-LGG dataset. Empirical tests demonstrate that SASG-GCN accurately classifies the subtypes of LGG. The accuracy of SASG-GCN achieves 93.62%, outperforming several other state-of-the-art classification methods. In-depth discussion and analysis reveal that the self-attention similarity-guided strategy improves the performance of SASG-GCN. The visualization revealed differences between different gliomas.