The free-space measurement system operating in 8GHz∼40GHz frequency range consists of two X-band ripples horn single-lens antennas, waveguide transmission segment, fixture, a mounting station, an Agilent N5225A network analyzer and a computer. A dual calibration technique of SOLT and GRL is used to eliminate errors due to multiple reflections via the surface of the sample. The complex permittivity is calculated from the S parameter of sample. Measurement results in 8GHz∼40GHz frequency range are reported for some absorbing material.