Computational drug repositioning aims to identify potential applications of existing drugs for the treatment of diseases for which they were not designed. This approach can considerably accelerate the traditional drug discovery process by decreasing the required time and costs of drug development. Tensor decomposition enables us to integrate multiple drug- and disease-related data to boost the performance of prediction. In this study, a nonnegative tensor decomposition for drug repositioning, NTD-DR, is proposed. In order to capture the hidden information in drug-target, drug-disease, and target-disease networks, NTD-DR uses these pairwise associations to construct a three-dimensional tensor representing drug-target-disease triplet associations and integrates them with similarity information of drugs, targets, and disease to make a prediction. We compare NTD-DR with recent state-of-the-art methods in terms of the area under the receiver operating characteristic (ROC) curve (AUC) and the area under the precision and recall curve (AUPR) and find that our method outperforms competing methods. Moreover, case studies with five diseases also confirm the reliability of predictions made by NTD-DR. Our proposed method identifies more known associations among the top 50 predictions than other methods. In addition, novel associations identified by NTD-DR are validated by literature analyses.