Correlations between spatial and spectral neighborhoods are utilized for compression of hyperspectral images. For multiple images taken at different times belonging to the same region, better compression performances can be obtained by exploiting temporal correlation. In this paper, multiple luminance transform based compression method is proposed for multi-temporal hyperspectral images. In the first step of the proposed method, target image is predicted from reference image using a linear transform. In the second step, difference between predicted and target image is compressed using 3D-DCT method. Prediction and compression performances of the proposed method are compared with the methods in the literature in terms of signal-to-noise ratio and entropy.