The wave transmission through a one-dimensional fractal system is numerically studied. The fractal system is constructed by arranging delta-function planar reflectors with a given polarizability value based on the middle-third Cantor set. The correlation dimension of a set of wave numbers corresponding to complete transmission and the intensity of scalar waves inside the system are calculated. It is found that the correlation dimension of the set depends on the polarizability of reflectors, but not on the number of reflectors, and that the intensity becomes more than ten thousand times larger than that of incident waves in some confined regions of the system. These results suggest possible application to a laser with low threshold and wave-guides for light in optical integrated circuits.