In this study, a novel group and region based parallel compression approach is proposed for hyperspectral imagery. The proposed approach contains two algorithms, which are clustering signal subspace projection (CSSP) and the maximum correlation band clustering (MCBC). The CSSP first divides the image into proper regions by transforming the high dimensional image data into one dimensional projection length. The MCBC partitions the spectral bands into several groups according to their associated band correlation for each image region. The image data with high degree correlations in spatial/spectral domains are then gathered in groups. Then, the grouped image data is further compressed by Principal Components Analysis (PCA)-based spectral/spatial hyper-spectral image compression techniques. Furthermore, to accelerate the computing efficiency, we present a parallel architecture of the proposed compression approach by using parallel cluster computing techniques. Simulation results performed on AVIRIS images have shown that the proposed group and region based approach performs better than standard 3D hyperspectral image compression. Moreover, the proposed approach achieves better computation efficiency than the direct combination of PCA and JPEG2000 under the same compression ratio.