An efficient lossless compression scheme of hyperspectral images based on one-band-prediction was proposed by using backward search in a context window to improve the compression ratio of the hyperspectral images. Firstly, the context window for a pixel to be tested was defined and the prediction reference value under testing was calculated. Then,the candidate predictors which were mostly closed to the prediction reference value were selected as the final prediction results of the pixel to be measured. Finally, the predicted residual image was coded by a first-order arithmetic to implement the image compression. The method proposed was used in the experiments on hyperspectral images from Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) 1997, and the results show that the method has obtained the best prediction results of backward search by optimizing the context window, equivalent coefficients and effective pixel thresholds. After coding by an arithmetic coder, the average compression ratio is 3.63。 The method has a lower computing complexity and smaller memory requirements, and outperforms all other lossless compression schemes for hyperspectral images that have been previously reported.