Based on the characteristics of hyperspectral images, three-dimensional set partitioned embedded zero-block coding (3D SPEZBC) algorithm for hyperspectral image compression is proposed. This algorithm adopts three-dimensional wavelet-packet transform to decorrelate hyperspectral image spectrally and spatially, and uses the quadtree partitioning method based on zero-block coding to process each of the two-dimensional subbands, and the context-based adaptive arithmetic coding scheme to further improve the coding performance. Experimental results show that the 3D SPEZBC algorithm has the same rate-distortion performances of three-dimensional embedded zero block coding (3D EZBC) algorithm, obviously outperforms three-dimensional set partitioned embedded block (3D SPECK) algorithm, three-dimensional set partitioning in hierarchical trees(3D SPIHT) algorithm and (AT-3D SPIHT) algorithm, and is slightly better than JPEG2000 multi-component (JPEG2000-MC) algorithm at different bit rate in the compression performances. Moreover, the 3D SPEZBC algorithm not only provides excellent rate-distortion performance, but also can save considerable memory requirement in comparison with the 3D EZBC algorithm.