An efficient lossless compression scheme for hyperspectral images using conventional recursive least-squares (CRLS) predictor with adaptive prediction bands is proposed. The proposed scheme first calculates the preliminary estimates to form the input vector of the CRLS predictor. Then the number of bands used in prediction is adaptively selected by an exhaustive search for the number that minimizes the prediction residual. Finally, after prediction, the prediction residuals are sent to an adaptive arithmetic coder. Experiments on the newer airborne visible/infrared imaging spectrometer (AVIRIS) images in the consultative committee for space data systems (CCSDS) test set show that the proposed scheme yields an average compression performance of 3.29 (bits/pixel), 5.57 (bits/pixel), and 2.44 (bits/pixel) on the 16-bit calibrated images, the 16-bit uncalibrated images, and the 12-bit uncalibrated images, respectively. Experimental results demonstrate that the proposed scheme obtains compression results very close to clustered differential pulse code modulation-with-adaptive-prediction-length, which achieves best lossless compression performance for AVIRIS images in the CCSDS test set, and outperforms other current state-of-the-art schemes with relatively low computation complexity.