Drug repositioning or repurposing refers to identifying new indications for existing drugs and clinical candidates. Predicting new drug-target interactions (DTIs) is of great challenge in drug repositioning. This tricky task depends on two aspects. The volume of data available on drugs and proteins is growing in an exponential manner. The known interacting drug-target pairs are very scarce. Besides, it is hard to select the negative samples because there are not experimentally verified negative drug-target interactions. Many computational methods have been proposed to address these problems. However, they suffer from the high rate of false positive predictions leading to biologically interpretable errors. To cope with these limitations, we propose in this paper an efficient computational method based on deep semi-supervised learning (DeepSS-DTIs) which is a combination of a stacked autoencoders and a supervised deep neural network. The objective of this approach is to predict potential drug targets and new drug indications by using a large scale chemogenomics data while improving the performance of DTIs prediction. Experimental results have shown that our approach outperforms state-of-the-art techniques. Indeed, the proposed method has been compared to five machine learning algorithms applied all on the same reference datasets of DrugBank. The overall accuracy performance is more than 98%. In addition, the DeepSS-DTIs has been able to predict new DTIs between approved drugs and targets. The highly ranked candidate DTIs obtained from DeepSS-DTIs are also verified in the DrugBank database and in literature.