In this work, we propose ZF-buffer algorithm in order to accelerate the intersection test of ray tracing. ZF-buffer is used in the preprocessing of ray tracing and records the pointer that points to a parent face of a depth value (z value) of an object determined in Z-buffer. As a result, the face that intersects with the first ray can be determined easily by using the pointer stored in F-buffer. Though ZF-buffer and vista-buffer resemble each other, the difference between the two methods is that what ZF-buffer records is not bounding volume but the pointer of a displayable face. We applied the ZF-buffer algorithm for the first ray to Utah teapot, which consists of 9216 polygons. By comparing the elapse time of our method with vista-buffer algorithm, we can acquire improvement in speed that it is 3 times faster than vista-buffer algorithm. We also try to apply our method to reflective objects.