Most compression methods for hyperspectral images have been optimized to minimize mean squared errors. However, this kind of compression method may not retain all discriminant information, which is important if hyperspectral images are to be used to distinguish among classes. In this paper, we propose a two-stage compression method for hyperspectral images with encoding residual discriminant information. In the proposed method, we first apply a compression method to hyperspectral images, producing compressed image data. From the compressed image data, we produce reconstructed images. Then we generate residual images by subtracting the reconstructed images from the original images. We also apply a feature extraction method to the original images, which produces a set of feature vectors. By applying these feature vectors to the residual images, we generate discriminant feature images which provide the discriminant information missed by the compression method. In the proposed method, these discriminant feature images are also encoded. Experiments with AVIRIS data show that the proposed method provides better compression efficiency and improved classification accuracy than other compression methods.