A lossless compression algorithm based on contents was proposed for hyperspectral images. An adaptive band selection algorithm was introduced to reduce the dimensionality of hyperspectral images, and a C-means algorithm was used to classify the spectral vectors resulting from dimensionality reduction unsupervisedly. Then, the reverse monotonic ordering method was taken to determine the prediction ordering, hyperspectral images were divided into groups adaptively according to the correlation between each adjacent bands, and the scheme of multi-band linear prediction was used to eliminate the spectral redundancy of the identical class. For each class, partial pixels within this class were selected to train optimal predictive coefficients, and predictive errors were compressed in lossless by JPEG-LS standard. Experiments were performed for the hyperspectral images acquired by an Airborne Visible/Infrared Imaging Spectrometer(AVIRIS) and an Operational Modular Imaging Spectrometer(OMIS). Experiental results show that the average compression ratio of the proposed algorithm can be improved about 0.11 and 0.7 respectively as compared with above algorithms without classification prediction.