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Abstract Predicting the interactions between drugs and targets plays an important role in the process of new drug discovery, drug repurposing (also known as drug repositioning). There is a need to develop novel and efficient prediction approaches in order to avoid the costly and laborious process of determining drug–target interactions (DTIs) based on experiments alone. These computational prediction approaches should be capable of identifying the potential DTIs in a timely manner. Matrix factorization methods have been proven to be the most reliable group of methods. Here, we first propose a matrix factorization-based method termed ‘Coupled Matrix–Matrix Completion’ (CMMC). Next, in order to utilize more comprehensive information provided in different databases and incorporate multiple types of scores for drug–drug similarities and target–target relationship, we then extend CMMC to ‘Coupled Tensor–Matrix Completion’ (CTMC) by considering drug–drug and target–target similarity/interaction tensors. Results: Evaluation on two benchmark datasets, DrugBank and TTD, shows that CTMC outperforms the matrix-factorization-based methods: GRMF, $$L_{2,1}$$-GRMF, NRLMF and NRLMF$$\beta $$. Based on the evaluation, CMMC and CTMC outperform the above three methods in term of area under the curve, F1 score, sensitivity and specificity in a considerably shorter run time.