In this work, we address the problem of improving robustness of convolutional neural networks (CNNs) to image distortion. We argue that higher moment statistics of feature distributions can be shifted due to image distortion, and the shift leads to performance decrease and cannot be reduced by ordinary normalization methods as observed in our experimental analyses. In order to mitigate this effect, we propose an approach base on feature quantization. To be specific, we propose to employ three different types of additional non-linearity in CNNs: I) a floor function with scalable resolution, ii) a power function with learnable exponents, and iii) a power function with data-dependent exponents. In the experiments, we observe that CNNs which employ the proposed methods obtain better performance in both generalization performance and robustness for various distortion types for large scale benchmark datasets. For instance, a ResNet-50 model equipped with the proposed method (+HPOW) obtains 6.95%, 5.26% and 5.61% better accuracy on the ILSVRC-12 classification tasks using images distorted with motion blur, salt and pepper and mixed distortions.