A KL(Kullback-Leibler) divergence multi-block moving window slow feature analysis method was proposed to solve the problems that the variable feature information cannot be fully utilized by the traditional block segmentation method based on experience, the local information is ignored by a single modeling method, and the off-line model cannot adapt to the time-varying characteristics. KL divergence was used to measure the distance between variables in the normal working condition data set, and the minimum error sum criterion was introduced to cluster, which was divided into two sub-blocks with the minimum distance. On this basis, the slow feature analysis method was utilized to model each sub-block, and the optimal model was obtained by updating the sampled data with moving window. Monitoring statistics were calculated respectively, and the fault monitoring results were fused with support vector data description to achieve fault diagnosis. The proposed method was applied to the monitoring of Tennessee Eastman process, and higher fault detection rate and lower false alarm rate are obtained, verify the feasibility and effectiveness of this method.