Abstract: A hyper-spectral image compression algorithm based on nonnegative tensor factorizations is proposed in this paper. First, every band of hyper-spectral images is decomposed by 2D 5/3 discrete wavelet transform to reduce the space redundancy of hyper-spectral images. Then, the four DWT sub-bands of the each level DWT for all spectral coverage are used as four tensors. And each sub-band tensor is decomposed by the proposed improved Hierarchical Alternating Least Squares (HALS) algorithm to reduce the spectra redundancy and the residual space redundancy. The algorithm can also protect the spectral information. Finally, the factorizations matrix is encoded by an entropy coder. The experimental results show that the proposed compression algorithm has good compressive property. In the compression ration range from 32:1 to 4:1, the average peak signal to noise ratio of proposed compression algorithm is higher than 40 dB. Compared with traditional approaches, the proposed method could improve the average PSNR by 1.499 dB. The compression performance of hyper-spectral image is effectively improved and the spectral information is protected.