In drug target interaction (DTI) the interactions of some (a subset) drugs on some (a subset) targets are known. The goal is to predict the interactions of all drugs on all targets. One approach is to formulate this as a matrix completion problem, where the matrix of interactions having drugs along the rows and targets along the columns is partially filled. So far standard matrix completion approaches such as nuclear norm minimization and matrix factorization have been used to address the problem. In this work, we propose a deep matrix factorization approach to improve the prediction results. Experiments have been performed on benchmark databases and comparison carried out with some state-of-the-art algorithms. Empirically our proposed deep method, outperforms all the techniques compared against.