In the study, an efficient compression approach, group and region based KLT (GR-KLT), is proposed for hyperspectral imagery. The GR-KLT contains one clustering signal subspace projection (CSSP) segmentation method and the maximum correlation band clustering (MCBC) method. The CSSP first divides the image into proper regions and the MCBC partitions the spectral bands into several groups according to their associated band correlation for each image region. By the way, the image is further compressed by the KLT-JPEG for each group in each image region. Furthermore, we develop a parallel architecture for the GR-KLT compression algorithm. Simulation results performed on AVIRIS images have demonstrated the efficiency of the proposed approaches.