The hyper-spectral image, which has two spatial dimensions and an additional spectral dimension, brings the greater amount of information than the grey level image but also the heavier spectral redundancy at the same time. Thus, it is a fact that hyper-spectral technology brings new challenges in image compression area. In this paper, we propose a hyper-spectral image compression algorithm based on tensor decomposition, in detail, the hyper-spectral image is represented as a 3-order-tensor, then the tensor decomposition technology is introduced to decompose the observed tensor data into a core tensor multiply by a series of projection matrices. By this way, the given hyper-spectral image is compressed into a low rank tensor, and it could be reconstructed by using the core tensor and the projection matrices. Experiments on real world hyper-spectral image datasets suggests that the proposed approach could reduce the hyper-spectral image to a low rate while keep the low reconstruction error.