Hyperspectral images (HSI) regularly contain hundreds of bands, which are of different importance in the application. Most HSI compression methods usually deal with most bands in the same way, and they do not take the difference of different bands into consideration, which may cause the loss of important spectral information. In order to preserve the spectral information of interest for applications, a new band-of-interest (BOI)-preserving-based HSI compression method is proposed. The conception of BOI is proposed because some bands are significant in the specific applications, and BOI selection methods are chosen according to application requirements. BOI selection is first performed according to application measurements. Then, BOI information is fed into recursive bidirection prediction (RBP) and set partition in hierarchical trees (SPIHT) compression scheme which uses RBP for spectral decorrelation followed by SPIHT algorithm for coding the resulting decorrelated residual images. More bits are allocated to BOI to preserve BOI by two approaches, respectively. Compress BOI and non-BOI bands directly with low distortion and high distortion, respectively, and compress all bands with low distortion and perform a postcompression truncation. Experiments are implemented with different settings using AVIRIS images. Results indicate that the proposed two methods both can achieve excellent compression efficiency and reconstructed quality. In addition, they can improve the application effect in both material classification and target recognition. Compared with non-BOI compression algorithm, at the compression ratio of 80, the proposed methods improve the classification accuracy by 2% and target recognition accuracy by 9%.