microRNAs (miRNAs) are non-coding RNA molecules that influence the development and progression of many diseases. Research have documented that miRNAs have a significant role in the prevention, diagnosis, and treatment of complex human diseases. Recently, scientists have devoted extensive resources to attempting to find the connections between miRNAs and diseases. Since the experimental methods used to discover that new miRNA-disease associations are time-consuming and expensive, many computational methods have been developed. In this research, a novel computational method based on matrix decomposition was proposed to predict new associations between miRNAs and diseases. Furthermore, the nuclear norm minimization method was employed to acquire breast cancer-associated miRNAs. We then evaluated the effectiveness of our method by utilizing two different cross-validation techniques and the results were compared to seven different methods. Moreover, a case study on breast cancer further validated our technique, confirming its predictive accuracy. These experimental results demonstrate that our method is a reliable computational model for uncovering potential miRNA-disease relationships.