The fuzzy self-organizing map neural network using kernel principal component analysis is presented and a hybrid-learning algorithm (KPCA-FSOM) divided into two stages is proposed to train this network. The first stage, the KPCA algorithm is applied to extract the features of nonlinear data. The second stage, combining both the fuzzy theory and locally-weight distortion index to extend SOM basic algorithm, the fuzzy SOM algorithm is presented to train the SOM network with features gained. A real life application of KPCA-FSOM algorithm in classifying data of acrylonitrile reactor is provided. The experimental results show this algorithm can obtain better clustering and network after training can more effectively monitor yields.