Abstract: The relativity between hyperspectral images of different waveband is differ from each other, contraposing this characteristic, this paper presents a lossless compression algorithm of hyperspectral image which is based on searching the optimal couple prediction wavebands. Through a searching model which is built by consulting the binary tree, two prediction wavebands are found, which have the most relativity to each basal waveband, and then the basal waveband is predicted using the two prediction wavebands. Experimental reault shows that, the compression algorithm has a primely compression performace compared with other compression algorithms present recently.