Automatic speech recognition (ASR) systems based on deep neural networks are weak against adversarial perturbations. We propose mixPGD adversarial training method to improve the robustness of the model for ASR systems. In standard adversarial training, adversarial samples are generated by leveraging supervised or unsupervised methods. We merge the capabilities of both supervised and unsupervised approaches in our method to generate new adversarial samples which aid in improving model robustness. Extensive experiments and comparison across various state-of-the-art defense methods and adversarial attacks have been performed to show that mixPGD gains 4.1% WER of better performance than previous best performing models under white-box adversarial attack setting. We tested our proposed defense method against both white-box and transfer based black-box attack settings to ensure that our defense strategy is robust against various types of attacks. Empirical results on several adversarial attacks validate the effectiveness of our proposed approach.