With the development of high-through sequencing technology and microbiology, many studies have evidenced that microbes are associated with human diseases, such as obesity, liver cancer, and so on. Therefore, identifying the association between microbes and diseases has become an important study topic in current bioinformatics. The emergence of microbe-disease association database has provided an unprecedented opportunity to develop computational method for predicting microbe-disease associations. In the study, we propose a low-rank matrix completion method (called MCHMDA) to predict microbe-disease associations by integrating similarities of microbes and diseases and known microbe-disease associations into a heterogeneous network. The microbe similarity is computed from Gaussian Interaction Profile (GIP) kernel similarity based on the known microbe-disease associations. Then, we further improve the microbe similarity by taking into account the inhabiting organs of these microbes in human body. The disease similarity is computed by the average of disease GIP similarity, disease symptom-based similarity, and disease functional similarity. Then, we construct a heterogeneous microbe-disease association network by integrating the microbe similarity network, disease similarity network, and known microbe-disease association network. Finally, a matrix completion method is used to calculate the association scores of unknown microbe-disease pairs by the fast Singular Value Thresholding (SVT) algorithm. Via 5-fold Cross Validation (5CV) and Leave-One-Out Cross Validation (LOOCV), we evaluate the prediction performances of MCHMDA and other state-of-the-art methods which include BRWMDA, NGRHMDA, LRLSHMDA, and KATZHMDA. On benchmark dataset HMDAD, the experimental results show that MCHMDA outperforms other methods in terms of area under the receiver operating characteristic curve (AUC). MCHMDA achieves the AUC values of 0.9251 and 0.9495 in 5CV and LOOCV, respectively, which are the highest values among the competing methods. In addition, we also further indicate the prediction generality of MCHMDA on an expanded microbe-disease associations dataset (HMDAD-SUP). Finally, case studies prove the prediction ability in practical applications.