In this paper, a robust classification-autoencoder (CAE) is proposed, which has strong ability to recognize outliers and defend adversaries. The main idea is to change the autoencoder from an unsupervised learning model into a classifier, where the encoder is used to compress samples with different labels into disjoint compression spaces and the decoder is used to recover samples from their compression spaces. The encoder is used both as a compressed feature learner and as a classifier, and the decoder is used to decide whether the classification given by the encoder is correct by comparing the input sample with the output. Since adversary samples are seemingly inevitable for the current DNN framework, the list classifier to defend adversaries is introduced based on CAE, which outputs several labels and the corresponding samples recovered by the CAE. Extensive experimental results are used to show that the CAE achieves state of the art to recognize outliers by finding almost all outliers; the list classifier gives near lossless classification in the sense that the output list contains the correct label for almost all adversaries and the size of the output list is reasonably small.