Recently, as a growing number of associations between microRNAs (miRNAs) and diseases are discovered, researchers gradually realize that miRNAs are closely related to several complicated biological processes and human diseases. Hence, it is especially important to construct availably models to infer associations between miRNAs and diseases. In this study, we presented Improved Graph Regression for miRNA-Disease Association Prediction (IGRMDA) to observe potential relationship between miRNAs and diseases. In order to reduce the inherent noise existing in the acquired biological datasets, we utilized matrix decomposition algorithm to process miRNA functional similarity and disease semantic similarity and then combining them with existing similarity information to obtain final miRNA similarity data and disease similarity data. Then, we applied miRNA-disease association data, miRNA similarity data and disease similarity data to form corresponding latent spaces. Furthermore, we performed improved graph regression algorithm in latent spaces, which included miRNA-disease association space, miRNA similarity space and disease similarity space. Non-negative matrix factorization and partial least squares were used in the graph regression process to obtain important related attributes. The cross validation experiments and case studies were also implemented to prove the effectiveness of IGRMDA, which showed that IGRMDA could predict potential associations between miRNAs and diseases.