With the rapid development of industrial processes, the complex nonlinear dynamic features of process data have created great challenges for deep learning models. However, existing deep learning models such as stacked autoencoder (SAE) mainly focus on capturing static data feature information while ignoring the extraction of dynamic data evolution pattern. To combat this issue, this paper proposes a novel deep learning model based on dynamic stacked autoencoder (DSAE) to collaboratively learn deep static and dynamic features of process data. Firstly, the sliding window technology is utilized to obtain temporal nearest neighbor samples within each time window. Then, multiple stacked autoencoder modules are utilized hierarchically to extract static features in each window. After that, the proposed dynamics feature extraction module is exploited to extract the local dynamics information of the data within each window. Finally, the learned dynamic and static features are collaboratively fused to build a soft sensor model for quality prediction tasks. To validate the superiority of the proposed model, it is applied to the simulation experiments of tobacco drying process and hydrocracking process. The experimental results show that the performance of the proposed model performs better than other methods.