Purified terephthalic acid (PTA) is an important product for the polyester and textile industry. In the industrial PTA-production process, 4-carboxybenzaldehyde (4-CBA) is a detrimental byproduct that can lower the polymerization rate and the average molecular weight of the polymer. Therefore, the content of 4-CBA in the final product can be used as a quality index to evaluate the current running status of the PTA-production process. However, because of the slow catalyst deactivation, this process is notable for its nonlinearity and dynamics. It is very difficult to obtain the 4-CBA-content values using traditional prediction methods from the process directly in real-time. For a better estimation of the status of the PTA-production process, a novel, online quality-prediction method based on modified regularized slow-feature analysis (ReSFA) is proposed in this paper for predicting the concentration of 4-CBA. The proposed method can handle the dynamics of the process better by exploring the temporal relationship of the input variables and incorporating the neighboring relationships of the input and output variables. Meanwhile, a modified just-in-time-learning method is introduced to deal with nonlinearity to improve online prediction performance. Finally, a case study is conducted with data sampled from a practical industrial terephthalic acid hydropurification process to demonstrate the effectiveness and superiority of the proposed method.