Prediction of drug-target interactions (DTIs) plays a significant role in drug development and drug discovery. Although this task requires a large investment in terms of time and cost, especially when it is performed experimentally, the results are not necessarily significant. Computational DTI prediction is a shortcut to reduce the risks of experimental methods. In this study, we propose an effective approach of nonnegative matrix tri-factorization, referred to as NMTF-DTI, to predict the interaction scores between drugs and targets. NMTF-DTI utilizes multiple kernels (similarity measures) for drugs and targets and Laplacian regularization to boost the prediction performance. The performance of NMTF-DTI is evaluated via cross-validation and is compared with existing DTI prediction methods in terms of the area under the receiver operating characteristic (ROC) curve (AUC) and the area under the precision and recall curve (AUPR). We evaluate our method on four gold standard datasets, comparing to other state-of-the-art methods. Cross-validation and a separate, manually created dataset are used to set parameters. The results show that NMTF-DTI outperforms other competing methods. Moreover, the results of a case study also confirm the superiority of NMTF-DTI.