Dimensionality reduction is a common preprocessing for hyperspectral image, and Kernel Principal Components Analysis(KPCA), as a common feature extraction method, makes use of nonlinear mapping to capture higher-order statistics of data. An optimization sample set algorithm, which is used in KPCA for dimensionality reduction of hyperspectral image was proposed. This algorithm picks sample set used in KPCA taking the statistics of the whole hyperspectral image into account simultaneously, and the minimum sample set with similar energy distribution of the full image is the final selection. The algorithm was implemented in IDL7.0 and tested by using the real hyperspectral image from Cuprite. The experiment results show that the new algorithm is able to save computing time significantly and perform better than conventional KPCA in dimensionality reduction.