Fault prediction is desired when a fault is detected for an industrial process, which can greatly enhance the reliability and safety of the overall system. Since independent component analysis (ICA) has been successfully applied to monitor non-Gaussian processes, it is promising to build a data-driven prediction technology based on the ICA framework. This paper considers the fault prediction issue with a kernel independent components analysis (KICA) model to deal with both nonlinear and non-Gaussian features from industrial data. First, the KICA model is used for fault detection and fault reconstruction, so that the magnitude of the fault can be estimated properly. Then, based on the autocorrelation characteristics of the fault magnitude sequence, a multi-layer hierarchical prediction model is used to predict the trend of the fault. Finally, the effectiveness of this framework is verified on the Tennessee Eastman process.