A compression algorithm based on 3D-DWT and listless 3D SPIHT in conjunction with Band of Interest (BOI) for hyperspectral images is presented. It is specially developed for the LASIS (Large Aperture Static Imaging Spectrometer) system according to its interference properties. Firstly, decompose the hyperspectral image sequences with asymmetric uniform-tree 3D-DWT. Secondly, protect its major hyperspectral coefficients by BOI method. Finally, give a modified listless 3DSPIHT algorithm to encode the transformed images. The numerical experiment results show that the Peak Signal-to-noise Ratio (PNSR) is more than 40 dB at 8:1 compression rate; and achieves an efficient protection of hyperspectral information.