Analysis of degraded ancient documents is challenging due to the severity and combination of degradation present in a single image. Ancient documents also suffer from additional noise during the digitalization process, particularly when digitalization is done using low-specification devices and/or under poor illumination conditions. The noises over the degraded ancient documents certainly cause a troublesome document analysis. In this paper, we propose a new noise-robust convolutional neural network (CNN) architecture for degradation classification of noisy ancient documents, which is called a degradation classification network (DCNet). DCNet was constructed based on the ResNet101, MobileNetV2, and ShuffleNet architectures. Furthermore, we propose a new self-transition layer following DCNet. We trained the DCNet using (1) noise-free document images and (2) heavy-noise (zero mean Gaussian noise (ZMGN) and speckle) document images. Then, we tested the resulted models with document images containing different levels of ZMGN and speckle noise. We compared our results to three CNN benchmarking architectures, namely MobileNet, ShuffleNet, and ResNet101. In general, the proposed architecture performed better than MobileNet, ShuffleNet, ResNet101, and conventional machine learning (support vector machine and random forest), particularly for documents with heavy noise.