In the paper, a new process monitoring approach is proposed for handling the multimode problem in the industrial processes. The original space can be separated into two different parts, which are the common part and the specific part. There are both similarity and dissimilarity in the underlying correlations of different modes, which play different roles in the industrial processes. Because the industrial processes have the non-Gaussian and nonlinear characteristics, modified kernel independent component analysis is used to monitor the multimode processes in this paper. The global multimode basis vector and the multimode sub-basis vector are obtained based on the modified KICA. Then, the common part and specific part in one mode are respectively analyzed. The proposed method is applied to monitor the continuous annealing process. The proposed approach effectively captures the non-Gaussian and nonlinear relationship in different modes in the industrial processes.