Composite electromagnetic wave absorbers made of a soft magnetic material (permalloy or sendust) and polystyrene resin were investigated . The volume mixture ratio of magnetic material was varied in the range from 18 vol% to 75 vol%. The composites with the low volume mixture ratio of soft magnetic material absorbed more than 99 % of electromagnetic wave power in the frequency range from 1 GHz to 10 GHz. The values of the real part r’ of the relative complex permeability r * for both magnetic materials were less than unity at frequencies above approximately 6 GHz as the volume mixture ratio of magnetic material increased. This result suggests the possible realization of an electromagnetic wave absorber that can operate above 10 GHz.