In many industries, the effective monitoring and control of batch processes is crucial to the production of high-quality materials. Several techniques using multivariate statistical analysis have been developed for monitoring and fault detection of batch processes. Multiway principal component analysis (MPCA) has shown a powerful monitoring performance in many industrial batch processes. However, it has shortcomings that all batch lengths should be equalized and future values of batches should be estimated for on-line monitoring. In order to overcome these drawbacks and obtain better monitoring performance, we propose a new statistical method for on-line batch process monitoring that uses different unfolding method and independent component analysis (ICA). If the measured data set contains non-Gaussian latent variables, the ICA solution can extract the original source signal to a much greater extent than the PCA solution since ICA involves higher-order statistics and is not based on the assumption that the latent variables follow a multivariate Gaussian distribution. The proposed monitoring method was applied to fault detection and identification in the simulation benchmark of the fed-batch penicillin production, which is characterized by some fault sources with non-Gaussian characteristics. The simulation results clearly show the power and advantages of the proposed method in comparison to MPCA.