A low-complexity three-dimensional image compression algorithm based on wavelet transforms and set-partitioning strategy is presented. The Subband Block Hierarchial Partitioning (SBHP) algorithm is modified and extended to three dimensions, and applied to every code block independently. The resultant algorithm, 3D-SBHP, efficiently encodes 3D image data by the exploitation of the dependencies in all dimensions, while enabling progressive SNR and resolution decompression and Region-of-Interest (ROI) access from the same bit stream. The code-block selection method by which random access decoding can be achieved is outlined.The resolution scalable and random access performances are empirically investigated. The results show 3D-SBHP is a good candidate to compress 3D image data sets for multimedia applications.