In this letter, we propose an efficient lossless compression algorithm for hyperspectral images; it is based on an adaptive spectral band reordering algorithm and an adaptive backward previous closest neighbor (PCN) prediction with error feedback. The adaptive spectral band reordering algorithm has some strong points. It can adaptively determine the range of spectral bands needed to be reordered, and it can efficiently find the optimum branches. Hyperspectral images have a large number of spectral bands, which express the same land cover structure and have high correlation. The adaptive backward PCN prediction with error feedback can sufficiently make use of this correlation. Experiments show that implementing both the reordering of the spectral bands before prediction and the prediction with error feedback improve compression performance