Principal component analysis (PCA) and kernel PCA (KPCA) are the state-of-art machine learning methods widely used in industrial process monitoring and fault detection field. However, these methods build shallow statistical models based on single layer of features and may not achieve the best monitoring performance. In order to sufficiently mine the intrinsic data features, a deep learning based nonlinear PCA method, referred to as deep PCA (DePCA), is proposed in this paper. Motivated by the idea of deep learning, a layer-wise statistical model structure is designed to extract multilayer data features, including both linear and nonlinear principal components. At each layer, two monitoring statistics are constructed to monitor the feature changes. For integrating the monitoring statistics of all feature layers, a Bayesian inference strategy is applied to convert the monitoring statistics into fault probabilities, which are weighted to form two probability-based comprehensive monitoring statistics for process fault detection. A case study using the benchmark Tennessee Eastman process demonstrates the superior performance of the proposed DePCA method over the traditional PCA and KPCA methods.