A new method for the lossless compression of the interferometer hyperspectral instrument Large Aperture Static Imaging Spectrometer (LASIS) data is presented in this paper. Differs from traditional hyperspectral instrument, the image captured by the two dimensional CCD detector of LASIS is no longer a normal image, but the two spatial information of the scene superimposed with interference fringes of equal thickness. There is a translation motion of the spatial information among each frame of LASIS data cube. Based on these unique data characteristics of LASIS and the recently presented CCSDS-123 lossless multispectral & Hyperspectral image compression standard, an improved predictor is designed for the prediction of LASIS data while using the standard. We perform several experiments on real data acquired by LASIS to investigate the performance of the proposed predictor. Experimental results show that the proposed predictor gives about 27.5% higher compression ratio than the default predictor of CCSDS-123 for lossless compression of LASIS data. In addition, the appropriate choice of several parameters of the proposed predictor are presented according to the experimental results. © 2018 SPIE.