To solve the transmission and storage problems resulting from massive hyperspectral remote sensing data, a lossless compression algorithm based on the optimal recursive bidirectional prediction for hyperspectral images is presented. Different compression models for each band are chosen according to their spectral correlation factors. If the spectral correlation factor is less than 0.9, the bzip2 compression model is chosen. Otherwise, the single band optimal previous prediction is performed on the reference band and the optimal recursive bidirectional prediction is performed on the non-reference band.Furthermore, the residual images are coded by JPEG-LS. The algorithms designed in this paper has been applied to the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data,the result shows that the average compression ratio is 3.217, which is 0.09-1.374 higher than those from other lossless compression algorithms. This method is fast and works efficiently, so it can be widely used in practice.