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Increasing evidences suggest that miRNAs play a key role in the occurrence and progression of many complex human diseases. Therefore, targeting dysregulated miRNAs with small molecule drugs in the clinical has become a new treatment. Nevertheless, it is high cost and time-consuming for identifying miRNAs-targeted with drugs by biological experiments. Thus, more reliable computational method for identification associations of drugs with miRNAs urgently need to be developed. In this study, we proposed an efficient method, called GNMFDMA, to predict potential associations of drug with miRNA by combining graph Laplacian regularization with non-negative matrix factorization. We first calculated the overall similarity matrices of drugs and miRNAs according to the collected different biological information. Subsequently, the new drug-miRNA association adjacency matrix was reformulated based on the K nearest neighbor profiles so as to put right the false negative associations. Finally, graph Laplacian regularization collaborative non-negative matrix factorization was used to calculate the association scores of drugs with miRNAs. In the cross validation, GNMFDMA obtains AUC of 0.9193, which outperformed the existing methods. In addition, case studies on three common drugs (i.e., 5-Aza-CdR, 5-FU and Gemcitabine), 30, 31 and 34 of the top-50 associations inferred by GNMFDMA were verified. These results reveal that GNMFDMA is a reliable and efficient computational approach for identifying the potential drug-miRNA associations., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Wang, Li, Lei, Ding and Xie.)