A lossless compression algorithm of hyper-spectral interference image based on principal-modulated prediction is proposed. Hyper-spectral interference images are divided into the space direction and the optical path difference(OPD) direction. In the space direction,a principal component prediction algorithm is used to reduce the inter-frame redundancies. And a modulated component prediction is used to reduce the spectral redundancies in the OPD direction. A two-step prediction algorithm is proposed for the principal component prediction. In the first step of prediction,a four order predictor is used to obtain a prediction reference value. In the second step,an 8-level lookup tables’ prediction algorithm is proposed and used to obtain the real-prediction. Then the final prediction is obtained through comparison between the real value and the reference prediction. A linearity prediction is used to obtain modulation prediction frame in the modulated component prediction. Finally,the final prediction frame is obtained through comparison between the principal component frame and the modulated component prediction frame. And the residual frame is obtained,which is encoded by an entropy coder. The experiments results show that the average compression ratio of proposed compression algorithm is reached to 3.05 bpp. Compared with traditional approaches,the proposed method can improve the average compression ratio by 0.14~2.94 bpp. They effectively improve the lossless compression ratio for hyper-spectral image lossless compression.