MicroRNA(miRNA) is a class of short non-coding RNAs with a length of about 22 nucleotides, which participates in various biological processes of cells. A number of studies have shown that miRNAs are closely related to the occurrence of cancer and various human diseases. Therefore, studying miRNA-disease associations is helpful to understand the pathogenesis of diseases as well as the prevention, diagnosis, treatment and prognosis of diseases. Traditional biological experimental methods for studying miRNA-disease associations have disadvantages such as expensive equipment, time-consuming and labor-intensive. With the rapid development of bioinformatics, more and more researchers are committed to developing effective computational methods to predict miRNA-disease associations in roder to reduce the time and money cost of experiments. In this study, we proposed a neural network-based deep matrix factorization method named NNDMF to predict miRNA-disease associations. To address the problem that traditional matrix factorization methods can only extract linear features, NNDMF used neural network to perform deep matrix factorization to extract nonlinear features, which makes up for the shortcomings of traditional matrix factorization methods. We compared NNDMF with four previous classical prediction models (IMCMDA, GRMDA, SACMDA and ICFMDA) in global LOOCV and local LOOCV, respectively. The AUCs achieved by NNDMF in two cross-validation methods were 0.9340 and 0.8763, respectively. Furthermore, we conducted case studies on three important human diseases (lymphoma, colorectal cancer and lung cancer) to validate the effectiveness of NNDMF. In conclusion, NNDMF could effectively predict the potential miRNA-disease associations.