Based on the concept of Equivalent Transformation Method of Material Constant (ETMMC), a thin and light weight EM-wave absorber is newly proposed. It becomes possible to merge both the competing characteristics of changing the matching frequency toward a higher frequency region by means of punching out small holes in the magnetic absorber and of changing the matching frequency toward a lower frequency region by attaching periodical conductive patterns to the surface of it. First, the ETMMC idea is introduced in this paper. The detailed matching characteristics of the present absorber are investigated based on FDTD analysis. The matching mechanism is clarified from input admittance chart viewpoints. The matching characteristics can be changed from 2.4 GHz to above 6.0 GHz using carbonyl iron with the thickness of 2 mm and improved below -20 dB.