Recently, the robustness of deep neural networks has drawn extensive attention due to the potential distribution shift between training and testing data (e.g., deep models trained on high-quality images are sensitive to corruption during testing). Many researchers attempt to make the model learn invariant representations from multiple corrupted data through data augmentation or image-pair-based feature distillation to improve the robustness. Inspired by sparse representation in image restoration, we opt to address this issue by learning image-quality-independent feature representation in a simple plug-and-play manner, that is, to introduce discrete vector quantization (VQ) to remove redundancy in recognition models. Specifically, we first add a codebook module to the network to quantize deep features. Then we concatenate them and design a self-attention module to enhance the representation. During training, we enforce the quantization of features from clean and corrupted images in the same discrete embedding space so that an invariant quality-independent feature representation can be learned to improve the recognition robustness of low-quality images. Qualitative and quantitative experimental results show that our method achieved this goal effectively, leading to a new state-of-the-art result of 43.1% mCE on ImageNet-C with ResNet50 as the backbone. On other robustness benchmark datasets, such as ImageNet-R, our method also has an accuracy improvement of almost 2%.