In some scientific visualization applications, very high resolution 3D data can be encountered, where the data size significantly exceeds the physical size of memory. Thus, space efficiency is an important issue in volume rendering. In addition, with the rapid development of network technology, many visualization applications involve remote access to data. Therefore, efficient transmission of volume data is also an important concern. This paper presents a method of directly rendering wavelet compressed volume data, which reduces the memory requirements, while keeps the voxel reconstruction (on- the-fly) overhead low. The volume data was decomposed by a wavelet transformation. The voxel values are reconstructed on- the-fly during the rendering process. In contrast to the point-wise reconstruction techniques that contain implicit reconstruction redundancy, an efficient block-wise reconstruction method is proposed in this paper. A significant improvement in computational performance is achieved by using a cache algorithm to temporarily retain the reconstructed blocks to be used by the adjacent rays. Further acceleration is achieved by an adaptive voxel reconstruction method, which is equivalent to the popular octree acceleration technique, but which is fully implemented within the frame work of the wavelet transformation.