On the basis of third-order predictor and backward pixel search technology (IP3-BPS), a lossless compression third-order predictor algorithm using three-stage prediction with adaptive predictor reordering was proposed to overcome the calibration-induced data correlation of hyperspectral images. Firstly, hyperspectral images were divided into groups adaptively according to the correlation factor between adjacent bands. Then using the calibration-induced data correlation and the band scaling factor, a recursive Bidirectional Pixel Search (RBPS) method and an adaptive band grouping method were proposed, respectively, for these groups with spectral correlation factor more than 0.9. The proposed algorithm takes the recursive bidirectional pixel search and the backward pixel search as the last two predictors, and adjusts adaptively their orders to achieve better prediction values. The experiments on the images from an Airborne Visible/Infrared Imaging Spectrometer (AVIRIS 1997) were performed. It shows that the average bit-rate of the proposed algorithm is 3.85 bpp, 0.07-1.28 bpp higher than those of other lossless compression algorithms. It is an effective lossless compression method for hyperspectral images in low computational complexity.