The non-Gaussian of the hyperspectral image can be well expressed by skewness and kurtosis, which highlight the target, texture and other anomaly information. They can be well applied to the band selection. In order to stand out the partial anomaly information better, the local joint skewness and kurtosis-based band selection for hyperspectral image is proposed on the basis of the global joint skewness-kurtosis figure. The bands of the original image are divided by the global joint skewness-kurtosis index into several subspaces. Then the template window of appropriate size is chosen and the local joint skewness-kurtosis index is calculated. All bands are traversed by this method. Finally, the accumulated local joint skewness-kurtosis index is calculated in order to complete the band selection. The band selection results show that the bands selected by the local joint skewness-kurtosis method are more widely distributed and the effect is better. The anomaly detection and fusion results show that the image obtained by the proposed method has great advantages in the evaluation of objective indicators.