How to select a combination of bands with a good classification effect from an image is a key issue in the task of hyperspectral image classification. Aiming at the above problems, a band selection algorithm based on the separability of single-band image categories and the correlation between bands is proposed. According to the principle of inter-class separability, the mean and standard deviation of all kinds of sample point matrices in single-band images are used to measure the inter-class separability of single-band images. Combined with the correlation coefficient between bands, the band combinations with good inter-class separability and low inter-band correlation are selected. Finally, the images before and after band selection of the proposed algorithm and the images after band selection of the adaptive band selection algorithm are classified by support vector machine. The classification results on Indian Pines and Salinas datasets show that when the number of spectral bands selected is 20 and the classification training set is randomly selected 20 sample points for each type of ground objects, the overall classification accuracy of the proposed algorithm is improved by 7.34 percentage points and 2.96 percentage points respectively compared with the adaptive band selection algorithm.