A hyper-spectral image lossless compression algorithm based on bi-directional lookup tables’(LUT) prediction of two steps is proposed,which combines intra-band and inter-band prediction to reduce the strong correlation of inter-band for hyper-spectral images.Firstly,the intra-band prediction is used only for the first image along the spectral line using a JPEG-LS median predictor.And the inter-band prediction is applied for other band images.A two-step and bi-directional prediction algorithm is proposed for the inter-band prediction.In the first step prediction,a bi-directional and four-order predictor is proposed,which is used to obtain a reference prediction value.In the second step prediction,an 8-level lookup tables’(LUT) prediction algorithm is proposed,which is used to obtain 8 values of LUT prediction.Then the final prediction is obtained through comparison between the 8 lookup tables’ values and the reference prediction value.Finally,an entropy coding is used to perform adaptive arithmetic coding on prediction residuals.The experimental results show that the average compression ratio of the proposed algorithm is up to 3.05 bpp.Compared with traditional approaches,the proposed method could improve the average compression ratio by 0.14-2.91 bpp.