Slow feature analysis (SFA) is being adopted in the process monitoring and fault diagnosis as a new latent variable extraction and dimension reduction method. As temporally relevant dynamic features extracted by SFA, slow features (SFs) can reveal typical systematic trends. However, SFA cannot resist the influence of outliers, which can deteriorate the performance of the SFA monitoring model since SFA considers that the modeling data contain only slow features and quickly varying noise. In this study, a robust SFA (RSFA) method based on the M-estimator is proposed, based on which a robust SFA monitoring model is established. Such a method can eliminate the steady and dynamic anomalies due to outliers while obtaining a precise estimation of normalization factors. It properly detects outliers in the eigendecomposition and replaces them with suitable values. Finally, the feasibility and effectiveness of the RSFA monitoring method are demonstrated by a numerical simulation and Tennessee Eastman (TE) benchmark process.