The accuracy of the process model directly affects the performance of the model-based controller. In zinc hydrometallurgy, the overall dynamics of the cobalt removal process can hardly be described by a fixed model since there are a series of interconnected reactors working together under time-varying inlet and reaction conditions. In this study, an interacting continuously stirred tank reactors (ICSTR) model is developed to describe the cooperative relationship of these cascaded reactors. Considering the time-varying inlet and reaction conditions, the reaction surface conversion coefficient is defined and incorporated into the ICSTR model, and the kernel partial least squares (KPLS) is employed to update the dynamic model online. The effectiveness of the time-varying ICSTR model is validated using industrial data. Based on the proposed time-varying ICSTR model, a predictive controller is designed to realize the optimal operation of the cobalt removal process. Simulation results indicate that compared with conventional predictive control and manual manipulation, the time-varying ICSTR model-based predictive control method can not only maintain the outlet cobalt ion concentration but also reduce the zinc dust dosage.