Ancient paintings are valuable historical heritages of human society with profound cultural connotations. However, the repairing of cracks by pasting rice paper on the back of paintings generates hidden strip information. To accurately extract the hidden strip information in ancient paintings, a method of hidden strip information extraction from hyperspectral images of ancient paintings is proposed. Firstly, we use the minimum noise fraction transform to remove the noise information and convert the image into bands arranged in order of decreasing signal-to-noise ratio. Secondly, we introduce the average gradient and cross-entropy as indicators to evaluate the informativeness of each band. A band that is richer in strip information has a larger gradient, which can be used as a reference for band selection. Finally, we combine the original image with the selected optimal band to complete the extraction of strip information. The results of our paper are expected to be useful in the protection, restoration, and identification of cultural relics.