1. A texture mapping system for generating pixels displayed on a screen by texture mapping, comprising a texture cache for storing texture image data fetched from a frame buffer memory with respect to one scanline, said texture cache comprising: a column structure including a tag region for storing an image coordinate value (u,v) of the texture image data, a refill line region for storing texture image data corresponding to the image coordinate value of the tag region, and an effective bit region for storing data indicating whether data of the refill line region is used for scanline texture mapping; and a row structure for storing texture image patch data to be texture mapped, wherein said row structure has a number rows which is equal to the number of texture image patch data with respect to an image of a maximum length covering at least one scanline to be texture mapped.