The search for new medicines demands a significant investment of resources, leading to a reassessment of strategies to enhance the efficiency of drug discovery. Recent progress in deep learning (DL) has shown promising developments in understanding Drug-Target Interactions (DTIs). In this paper, we propose a novel methodology for Drug-Target Interaction (DTI) prediction, leveraging the Transformer architecture. Our methodology integrates a Transformer and a Graph Transformer, designed to learn the feature representation from protein and compound molecules. This combination of graph and attention-based mechanism enhances the performance of interaction predictions by capturing dependencies at different levels of abstraction. We evaluated our model on benchmark datasets, Human and C. elegans, comparing its performance with state-of-the-art DL models. The results demonstrate the effectiveness of our DL model in DTI prediction, surpassing the performance of other DL-based methods on both datasets.