In the modern chemical industry, the process data collected are high-dimensional and complex. All measured variables are usually incorporated in statistical process monitoring models because these models generally perform dimension reduction. However, if modeling involves variables that do not contain useful information about faults, that is, variables that are not relevant to faults, monitoring performance may be degraded. In typical process monitoring methods, offline modeling only uses normal data without any fault information, making monitoring performance unlikely to be optimal. Hence, a novel stacked sparse autoencoder (SSAE) monitoring model based on fault-related variable selection was proposed. From the point of view that correlation characteristics between measured variables will change when faults occur, strongly fault-related variables are selected. Mutual information was used to calculate correlations between measured variables, including normal and fault data. Euclidean distance was adopted as a similarity index to measure the similarity between each correlation vector of measured variables in a normal state and that in a fault state. Only variables strongly related to fault effects were retained, and other uninformative variables were excluded from model development. Then, SSAEs were used to construct a monitoring model for selected data. The proposed method can utilize historical fault data to select strongly fault-related variables, making the model contain useful process information and features extracted by SSAE have high interpretability. A case study on the Tennessee–Eastman process demonstrated its availability.