We present a novel approach for GPU-based high-quality volume rendering of large out-of-core volume data. By focusing on the locations and costs of ray traversal, we are able to significantly reduce the rendering time over traditional algorithms. We store a volume in an octree (of bricks); in addition, every brick is further split into regular macrocells. Our solutions move the branch-intensive accelerating structure traversal out of the GPU raycasting loop and introduce an efficient empty-space culling method by rasterizing the proxy geometry of a view-dependent cut of the octree nodes. This rasterization pass can capture all of the bricks that the ray penetrates in a per-pixel list. Since the per-pixel list is captured in a front-to-back order, our raycasting pass needs only to cast rays inside the tighter ray segments. As a result, we achieve two levels of empty space skipping: the brick level and the macrocell level. During evaluation and testing, this technique achieved 2 to 4 times faster rendering speed than a current state-of-the-art algorithm across a variety of data sets.