Motivation: There is growing evidence showing that the dysregulations of miRNAs cause diseases through various kinds of the underlying mechanism. Thus, predicting the multiple-category associations between microRNAs (miRNAs) and diseases plays an important role in investigating the roles of miRNAs in diseases. Moreover, in contrast with traditional biological experiments which are time-consuming and expensive, computational approaches for the prediction of multicategory miRNA-disease associations are time-saving and cost-effective that are highly desired for us. Results: We present a novel data-driven end-to-end learning-based method of neural multiple-category miRNA-disease association prediction (NMCMDA) for predicting multiple-category miRNA-disease associations. The NMCMDA has two main components: (i) encoder operates directly on the miRNA-disease heterogeneous network and leverages Graph Neural Network to learn miRNA and disease latent representations, respectively. (ii) Decoder yields miRNA-disease association scores with the learned latent representations as input. Various kinds of encoders and decoders are proposed for NMCMDA. Finally, the NMCMDA with the encoder of Relational Graph Convolutional Network and the neural multirelational decoder (NMR-RGCN) achieves the best prediction performance. We compared the NMCMDA with other baselines on three experimental datasets. The experimental results show that the NMR-RGCN is significantly superior to the state-of-the-art method TDRC in terms of Top-1 precision, Top-1 Recall, and Top-1 F1. Additionally, case studies are provided for two high-risk human diseases (namely, breast cancer and lung cancer) and we also provide the prediction and validation of top-10 miRNA-disease-category associations based on all known data of HMDD v3.2, which further validate the effectiveness and feasibility of the proposed method.