Numerous investigations increasingly indicate the significance of microRNA (miRNA) in human diseases. Hence, unearthing associations between miRNA and diseases can contribute to precise diagnosis and efficacious remediation of medical conditions. The detection of miRNA-disease linkages via computational techniques utilizing biological information has emerged as a cost-effective and highly efficient approach. Here, we introduced a computational framework named ReHoGCNES, designed for prospective miRNA-disease association prediction (ReHoGCNES-MDA). This method constructs homogenous graph convolutional network with regular graph structure (ReHoGCN) encompassing disease similarity network, miRNA similarity network and known MDA network and then was tested on four experimental tasks. A random edge sampler strategy was utilized to expedite processes and diminish training complexity. Experimental results demonstrate that the proposed ReHoGCNES-MDA method outperforms both homogenous graph convolutional network and heterogeneous graph convolutional network with non-regular graph structure in all four tasks, which implicitly reveals steadily degree distribution of a graph does play an important role in enhancement of model performance. Besides, ReHoGCNES-MDA is superior to several machine learning algorithms and state-of-the-art methods on the MDA prediction. Furthermore, three case studies were conducted to further demonstrate the predictive ability of ReHoGCNES. Consequently, 93.3% (breast neoplasms), 90% (prostate neoplasms) and 93.3% (prostate neoplasms) of the top 30 forecasted miRNAs were validated by public databases. Hence, ReHoGCNES-MDA might serve as a dependable and beneficial model for predicting possible MDAs.