A Cantor fractal film set has been designed. The set shows a good absorption and very low reflection of electro-magnetic waves. The reflectivity of the film set has been calculated analytically based on a simplified model. A group of criterions for the selection of suitable materials for the set layers have been suggested according to the analytic results. Some example sets that are formed by ideal or practical materials with the criterions have been discussed. Our numerical computation has shown that the set averaged reflectivity decreases and its reflection spectrum becomes more even when the total degree number of the fractal increases. The lowest averaged reflectivity obtained is 0.01.