In order to resolve the difficulty in hardware implementation, lower compression ratio and time consuming for the whole hyperspectral image lossless compression algorithm based on the prediction, transform, vector quantization and their combination, a hyperspectral image lossless compression algorithm for space-borne application was proposed in the present paper. Firstly, intra-band prediction is used only for the first image along the spectral line using a median predictor. And inter-band prediction is applied to other band images. A two-step and bidirectional prediction algorithm is proposed for the inter-band prediction. In the first step prediction, a bidirectional and second order predictor proposed is used to obtain a prediction reference value. And a improved LUT prediction algorithm proposed is used to obtain four values of LUT prediction. Then the final prediction is obtained through comparison between them and the prediction reference. Finally, the verification experiments for the compression algorithm proposed using compression system test equipment of XX-X space hyperspectral camera were carried out. The experiment results showed that compression system can be fast and stable work. The average compression ratio reached 3.05 bpp. Compared with traditional approaches, the proposed method could improve the average compression ratio by 0.14~2.94 bpp. They effectively improve the lossless compression ratio and solve the difficulty of hardware implementation of the whole wavelet-based compression scheme.