The principal component analysis (PCA), a classical linear feature transformation method based on mathematical statistics, is effective in the analysis of linear data. Nevertheless, PCA is likely to result in distortion and loss of data information for non-linear hyperspectral Remote Sensing（RS）image data. In this paper, the fuzzy mathematical theory and the theory of kernel in pattern recognition is proposed for the purpose of effectively overcoming the shortcomings of traditional PCA. The test results show that the fuzzy kernel principal component analysis (FKPCA) designed in this paper can acquire competitive image feature extraction results.