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Deep neural networks have become popular in many supervised learning tasks, but they may suffer from overfitting when the training dataset is limited. To mitigate this, many researchers use data augmentation, which is a widely used and effective method for increasing the variety of datasets. However, the randomness introduced by data augmentation causes inevitable inconsistency between training and inference, which leads to poor improvement. In this paper, we propose a consistency regularization framework based on data augmentation, called CR-Aug, which forces the output distributions of different sub models generated by data augmentation to be consistent with each other. Specifically, CR-Aug evaluates the discrepancy between the output distributions of two augmented versions of each sample, and it utilizes a stop-gradient operation to minimize the consistency loss. We implement CR-Aug to image and audio classification tasks and conduct extensive experiments to verify its effectiveness in improving the generalization ability of classifiers. Our CR-Aug framework is ready-to-use, it can be easily adapted to many state-of-the-art network architectures. Our empirical results show that CR-Aug outperforms baseline methods by a significant margin.