The rise of social media has made information exchange faster and easier among the people. However, in recent times, the use of offensive language has seen an upsurge in social media. The main challenge for a service provider is to correctly identify such offensive posts and take necessary action to monitor and control their spread. In this work, we try to address this problem by using sophisticated deep learning techniques like LSTM, Bidirectional LSTM and Bidirectional GRU. Our proposed approach solves 3 different Sub-tasks provided in the SemEval-2019 task 6 which incorporates identification of offensive tweets as well as their categorization. We obtain significantly better results in the leader-board for Sub-task B and decent results for Sub-task A and Subtask C validating the fact that the proposed models can be used for automating the offensive post-detection task in social media.