Traditionally, independent component analysis (ICA) as a multivariate statistical process monitoring (MSPM) method has attracted considerable attention due to its excellent ability in analysis of non-Gaussian datasets. However, it may degrade fault detection performance for multimode operating process because of its assumption of one single steady mode. In order to supervise the non-Gaussian process with multiple steady modes more effectively, this paper proposes a process monitoring method based on local entropy independent component analysis (LEICA). This method applies local probability density estimation to remove the effects of multimode characteristics. Furthermore, information entropy theory is used to extract the feature information of process data by calculating their local information entropies. Based on these local entropy data, ICA is applied to establish the local entropy component model for fault detection. Lastly, a numerical example and the Tennessee Eastman (TE) process are used to verify the proposed method and the results demonstrate the superiority of LEICA method.