Deep learning systems aim at using hierarchical models to learning high-level features from low-level features. The progress in deep learning is great in recent years. The robustness of the learning systems with deep architectures is however rarely studied and needs further investigation. In particular, the mean square error (MSE), a commonly used optimization cost function in deep learning, is rather sensitive to outliers (or impulsive noises). Robust methods are needed to improve the learning performance and immunize the harmful influences caused by outliers which are pervasive in real-world data. In this paper, we propose an efficient and robust deep learning model based on stacked auto-encoders and Correntropy-induced loss function (CLF), called CLF-based stacked auto-encoders (CSAE). CLF as a nonlinear measure of similarity is robust to outliers and can approximate different norms (from to ) of data. Essentially, CLF is an MSE in reproducing kernel Hilbert space. Different from conventional stacked auto-encoders, which use, in general, the MSE as the reconstruction loss and KL divergence as the sparsity penalty term, the reconstruction loss and sparsity penalty term in CSAE are both built with CLF. The fine-tuning procedure in CSAE is also based on CLF, which can further enhance the learning performance. The excellent and robust performance of the proposed model is confirmed by simulation experiments on MNIST benchmark dataset.