Since the hyperspectral images (HSI) could provide much more useful discriminative information that cannot be obtained by the conventional imaging techniques, the hyper-spectral imaging technology was widely used in remote sensing area and recently used in many other aspects, such as the biological images recognition. However, most of the time, the size of hyperspectral data is so large that to process these data is both time-consuming and space-consuming. In this paper, a multiway tensor projection (MTP) algorithm is proposed as an extension to the conventional PCA for hyperspectral data compression and reconstruction. Technologically speaking, MTP carries out a tensor data compression in all the modes simultaneously to seek a projection matrix along each order to make sure that the projected core tensor can preserve most of the information present in the original tensor. Since the MTP algorithm uses the arbitrary order tensor as the input, it can preserve the structure information not only among the rows and columns but also among the spectral channels as much as possible and without vectorization. Numerous experiments on hyperspectral biological databases show that the MTP algorithm has better compression performance than PCA in many aspects.