Several optimization techniques have been proposed for volume ray casting, but these cannot achieve real-time frame rates. In addition, it is difficult to apply them to some applications that require perspective projection. Recently, hardware-based methods using 3D texture mapping are being used for real-time volume rendering. Although rendering speed approaches real time, the larger volumes require more swapping of volume bricks for the limited texture memory. Also, image quality deteriorates compared with that of conventional volume ray casting. In this paper, we propose a data structure for real-time volume ray casting named PERM (Precomputed dEnsity and gRadient Map). The PERM stores interpolated density and gradient vector for quantized cells. Since the information requiring time-consuming computations is stored in the PERM, our method can ensure interactive frame rates on a consumer PC platform. Our method normally produces high-quality images because it is based on conventional volume ray casting.