Effective fusion of multimodal magnetic resonance imaging (MRI) is of great significance to boost the accuracy of glioma grading thanks to the complementary information provided by different imaging modalities. However, how to extract the common and distinctive information from MRI to achieve complementarity is still an open problem in information fusion research. In this study, we propose a deep neural network model termed as multimodal disentangled variational autoencoder (MMD-VAE) for glioma grading based on radiomics features extracted from preoperative multimodal MRI images. Specifically, the radiomics features are quantized and extracted from the region of interest for each modality. Then, the latent representations of variational autoencoder for these features are disentangled into common and distinctive representations to obtain the shared and complementary data among modalities. Afterwards, cross-modality reconstruction loss and common-distinctive loss are designed to ensure the effectiveness of the disentangled representations. Finally, the disentangled common and distinctive representations are fused to predict the glioma grades, and SHapley Additive exPlanations (SHAP) is adopted to quantitatively interpret and analyze the contribution of the important features to grading. Experimental results on two benchmark datasets demonstrate that the proposed MMD-VAE model achieves encouraging predictive performance (AUC:0.9939) on a public dataset, and good generalization performance (AUC:0.9611) on a cross-institutional private dataset. These quantitative results and interpretations may help radiologists understand gliomas better and make better treatment decisions for improving clinical outcomes.