Abstract: In the compressive sensing theory, the robust reconstruction of signals can be obtained from far fewer measurements than those obtained by the Nyquist theorem. Thus, it has a great potential in the onboard compression of hyperspectral images using minimal computational resources and storage memory. In this paper, a compressive-sensing-based hyperspectral image compression method was presented using spectral unmixing. At the encoder, the original image was compressed acquired by spatial sampling and spectral sampling, respectively. Then, the spectral and spatial correlation of the compressed data were studied. To improve the compression performance, spectral linear prediction was used to remove the spectral correlation, and the predictive errors were compressed by JPEG-LS in a lossless manner to generate the final bit-streams. At the decoder, the bit-streams were first decoded to obtain the sampled data. Then, a spectral unmixing technique was employed to reconstruct the original hyperspectral image, which can avoid the defect of conventional compressed sensing reconstruction. Experiments on data from the Airborne Visible/Infrared Imaging Spectrometer sensor show that the proposed algorithm provides better compression performance than JPEG2000 and DCT-JPEG2000 with a lower computational complexity.