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A novel hyperspectral-image lossless compression scheme in the wavelet domain is proposed in this letter. This scheme is based on the context-based adaptive classified arithmetic-coding technique. The adaptive classified scheme divides each of the residual images between the two adjacent wavelet images into different classes, resulting in not only skipping the coding of a lot of insignificant zeros but also making the similar coefficients cluster together. Through experiments, we found that, when similar coefficients are clustered together, the arithmetic coding can achieve a higher performance than no clustering. Therefore, we can say that the adaptive classified scheme makes a better use of the characteristics of hyperspectral images and the characteristics of the arithmetic-coding technique. Experiments show that our proposed scheme is capable of providing high compression performance.