Sign language plays a pivotal role in the lives of impaired people having speaking and hearing disabilities. They can convey messages using hand gesture movements. American Sign Language (ASL) recognition is challenging due to the increasing intra-class similarity and high complexity. This paper used a deep convolutional neural network for ASL alphabet recognition to overcome ASL recognition challenges. This paper presents an ASL recognition approach using a deep convolutional neural network. The performance of the DeepCNN model improves with the amount of given data; for this purpose, we applied the data augmentation technique to expand the size of training data from existing data artificially. According to the experiments, the proposed DeepCNN model provides consistent results for the ASL dataset. Experiments prove that the DeepCNN gives a better accuracy gain of 19.84%, 8.37%, 16.31%, 17.17%, 5.86%, and 3.26% as compared to various state-of-the-art approaches.