Growing evidence indicates that the development and progression of multiple complex diseases are influenced by microRNA (miRNA). Identifying more miRNAs as biomarkers for clinical diagnosis, treatment and prognosis is vital to promote the development of bioinformatics and medicine. Considering that the traditional biological experimental methods are generally time-consuming and expensive, high-efficient computational methods are encouraged to uncover potential disease-related miRNAs. In this paper, FCGCNMDA is presented to predict latent miRNA-disease associations by utilizing fully connected graph convolutional networks. Specially, our method first constructs a fully connected graph in which edge weights represent correlation coefficient between any two pairs of miRNA-disease pair, and then feeds this fully connected graph along with miRNA-disease pairs feature matrix into a two-layer graph convolutional networks (GCN) for training. At last, we utilize the trained network to predict the scores for unknown miRNA-disease pairs. As a result, FCGCNMDA achieves AUC value of 92.85 +/- 0.71% and AUPRC value of 92.55% in HMDD v2.0 based on five-fold cross validation. Moreover, case studies on Lymphoma, Breast Neoplasms and Prostate Neoplasms shown that 98%, 98%, 98% of the top 50 selected miRNAs were validated by recent experimental evidence. From above results, we can deduce that FCGCNMDA can be regarded as reliable method for potential miRNA-disease associations prediction.