The data collected from modern industrial processes always have nonlinear and dynamic characteristics. The recently developed deep neural network method, stacked denoising auto-encoder (SDAE), can extract robust nonlinear latent variables from data against noise. However, it leaves the dynamic relationship unconsidered. To solve this problem, a novel algorithm named the recursive stacked denoising auto-encoder (RSDAE) is proposed. To learn the dynamic relationship, the RSDAE focuses on the predictability of the latent variables in the recurrence to contain the most dynamic variations. After the dynamic variations are extracted by the RSDAE, there is little autocorrelation left in the residuals. Then, the residuals can be monitored by principal component analysis (PCA). For the purpose of process monitoring, corresponding fault detection statistics are developed based on the RSDAE. Finally, a numerical case and the Tennessee Eastman process benchmark are used to demonstrate the effectiveness of the proposed algorithm.