Ray tracing requires many ray-object intersection tests. A way of reducing the number of ray-object intersection tests is to subdivide the space occupied by objects into many nonoverlapping subregions, called voxels, and to construct an octree for the subdivided space. 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.