Identification of potential drug-associated indications is critical for either approved or novel drugs in drug repositioning. Current computational methods based on drug similarity and disease similarity have been developed to predict drug-disease associations. When more reliable drug- or disease-related information becomes available and is integrated, the prediction precision can be continuously improved. However, it is a challenging problem to effectively incorporate multiple types of prior information, representing different characteristics of drugs and diseases, to identify promising drug-disease associations. In this study, we propose an overlap matrix completion (OMC) for bilayer networks (OMC2) and tri-layer networks (OMC3) to predict potential drug-associated indications, respectively. OMC is able to efficiently exploit the underlying low-rank structures of the drug-disease association matrices. In OMC2, first of all, we construct one bilayer network from drug-side aspect and one from disease-side aspect, and then obtain their corresponding block adjacency matrices. We then propose the OMC2 algorithm to fill out the values of the missing entries in these two adjacency matrices, and predict the scores of unknown drug-disease pairs. Moreover, we further extend OMC2 to OMC3 to handle tri-layer networks. Computational experiments on various datasets indicate that our OMC methods can effectively predict the potential drug-disease associations. Compared with the other state-of-the-art approaches, our methods yield higher prediction accuracy in 10-fold cross-validation and de novo experiments. In addition, case studies also confirm the effectiveness of our methods in identifying promising indications for existing drugs in practical applications.