As one of biomarkers of diseases, dysregulation of miRNAs is closely related to the occurrence and development of various human diseases. Identifying disease-related miRNAs can contribute to a deeper understanding of the pathological mechanisms of diseases and promote their treatment. Thus, there is an urgent need to develop effective computational methods for predicting potential miRNA-disease associations, which can serve as supplements to time-consuming and labor-intensive biological experimental methods. Although existing Graph Neural Network based methods have achieved good performance, the learning of comprehensive and high-quality miRNAs and diseases feature representations is still a challenge for these methods, as they typically extract information from only one of the local or global perspective. In this study, we propose a new graph representation learning method named LGFMDA for miRNA-disease association prediction. We first construct an attributed bipartite graph by the associations between miRNAs and diseases as well as their similarities. Then, we learn node feature representations from both local and global perspectives, and fuse the two types of features to obtain deep and representative feature embeddings of miRNA and disease nodes. Specifically, we compute an adaptive feature propagation depth for each node in the graph to fully aggregate local neighbourhood information, while global features are captured using the improved graph transformer framework. Finally, the feature representations of miRNA and disease pairs are fed into a MLP classifier to calculate association probabilities. In the five-fold cross-validation, LGFMDA achieves the AUC of 0.9561 and AUPR of 0.9546, outperforming seven state-of-the-art methods. The case study also further validate the performance of LGFMDA in practical applications. The source codes are available at https://github.com/LabBioMedCoder/LGFMDA. .