Slowly varying process variations represented by slow features, which reflect the inherent dynamics of chemical processes, are revealed to be advantageous for quality prediction. However, if slow features are extracted from process variables as predictors without the supervision of quality indices, some obvious disadvantages are observed: (1) low quality interpretation and redundant slow features since quality information is not considered for feature extraction; (2) a lack of analysis to investigate the relationship between slow features and quality interpretation, especially for different types of quality indices. To solve the above-mentioned problems, a new soft-sensor algorithm, quality-relevant slow feature regression (QSFR), is proposed in the present work. It defines a new objective function by concurrent consideration of slowness and quality interpretation, yielding more meaningful features as predictors to interpret quality index. On the basis of this, a critical feature selection strategy is proposed based on quality interpretation to determine the retained features for regression. Moreover, an in-depth analysis of the properties of retained features is provided to reveal the hidden mechanism and how the slow time-varying process variations influence the quality interpretation. This algorithm can extract more powerful features as predictors and enhance understanding of inherent nature of slow features. Finally, the feasibility and performance of the proposed method are well illustrated for a well-known benchmark process and a real chemical process. The developed QSFR algorithm performs better than traditional slow feature regression method, in which the values of RMSE of three specific quality indices have been reduced by 8.87%, 16.60%, and 3.40%, respectively. (C) 2019 Elsevier Ltd. All rights reserved.