In this paper, for compression and transmission of 3D image, we propose an algorithm which executes 3D discrete cosine transform(DCT) for 3D images, hierarchically segments 3D blocks of an image in comparison with the original image and executes finite-state vector quantization(FSVQ) for each 3D block. Using 3D DCT coefficient feature, a 3D image is segmented hierarchically into large smooth blocks and small edge blocks, then the block hierarchy informations are transmitted. The codebooks are constructed for each hierarchical blocks respectively, the encoder transmits codeword index using FSVQ for reducing encoded bit with hierarchical segmentation information. The new algorithm suggested in this paper shows that the quality of Small Lobster and Head image increased by 1,91 dB and 1.47 dB respectively compared with those of HFSVQ.