Ray tracing requires many ray-obect intersection tests, A way of reducing the number of ray-object intersection tests is to subdivide the space occupied by objects into many non overlapping subregions, called voxels, and to construct an octree for the subdivided space. In this paper, we propose the Octree-R, an octree-variant data structure for efficient ray tracing. The algorithm for constructing the Octree-R first estimates the number of ray-object intersection tests. Then, it partitions the space along the plane that minimizes the estimated number of ray-object intersection tests. We present the results of experiments for verifying the effectiveness of the Octree-R. In the experiment, the Octree-R provides a 4% to 47% performance gain over the conventional octree. The result shows the more skewed the object distribution (as is typical for real data), the more performance gain the Octree-R achieves.