An approach for compression of hyper-spectral image based on classification of sub-bands was proposed firstly. The wavelet decomposition was carried out and the sub-bands were partitioned into sub-blocks. Then sub-blocks were classified based on their activity. Based on classification, the algorithm uses prediction to remove the spectral redundancy, in which the algorithm computes the predictor for each class to reflect local correlation in sub-band images. Then the uniform trellis-coded quantization is used to quantize the error images. At last, entropy encoding of the quantized codeword is performed by adaptive arithmetic encoding. To optimally allocate bits through all series of coefficients, an algorithm for bit allocation based on statistic characteristic of the series of coefficients and R-D characteristic of trellis-coded quantizer was proposed. The experiments show that the approach can efficiently compress hyper-spectral remote sensing images, and the excellent performance of the proposed algorithm is demonstrated.