Hyperspectral image compression is an important task, where the aim is to store or transmit data in an efficient way. Hyperspectral images are mostly captured by a sensor system that includes multiple imaging sensors covering different regions of the electromagnetic spectrum. Misalignment of multiple imaging sensors produces boresight effect, and this problem can degrade band prediction performance noticeably. Another problem is prediction of blurry band images. In order to gain robustness to these problems, bimodal conventional recursive least-squares (B-CRLS) prediction method is proposed for the lossless compression of hyperspectral images. Two prediction modes are defined: spectral and spatio-spectral. B-CRLS method has a two-step process. First, mode selection is carried out for each band. Afterwards, final band image is predicted by using the selected mode, and the residual images are encoded with an arithmetic encoder. The proposed method is compared to adaptive-length CRLS, fixed-length CRLS, and other well-known prediction methods. Experiments have been performed on uncalibrated and calibrated hyperspectral images. Obtained results show that the proposed method achieves competitive compression performance with the state-of-the-art while providing relatively lower-computation times.