An approach for compression of hyper-spectral images based on wavelet trellis-coded quantization is proposed. Processing of spectral and spatial redundancy make up the main ingredients of compression of hyper-spectral image. Firstly, the proposed algorithm takes advantage of spectral difference pulse code modulation (DPCM) to remove the spectral redundancy, then the discrete wavelet transform is carried out over the error images resulted from DPCM and trellis-coded quantization with uniform threshold value is adopted to quantize the sub-band images. At last, entropy encoding of quantized code-words is performed by adaptive arithmetic encoding. To compute optimal quantization thresholds in rate-distortion sense for each sub-band of all spectral bands, an algorithm for bit allocation based on sub-band statistic characteristic and R-D characteristic of trellis-coded quantization is also desigued. In the experiments, excellent performance of the proposed algorithm is demonstrated. For the hyper-spectral image of experiment, the PSNR of the algorithm is 37.1 dB at the compression ratio of 32. This shows that the approach can efficiently compress hyper-spectral image and be suitable for the applications of hyper-spectral images compression.