Abstract: A hyperspectral image lossless compression algorithm based on multi-band prediction is proposed in this paper. Considering that as the spectral resolution of hyperspectral images increases, its spectral correlation becomes more and more significant, a group of prediction coefficients are derived, which are able to make use of multi-band to predict the current band linearly. And then a fast algorithm is given to solve the coefficients of the predictor. Experiments show that, with AVIRIS, the ratio of the algorithm is competitive and it runs fast, so it works efficiently in practice.