In a free-space method using a pair of horn antennas with dielectric lenses, we demonstrated that the permittivity of a sample can be estimated with good accuracy by equalizing a measured transmission coefficient of a sample to a transmission coefficient for a Gaussian beam, which is approximately equal to the transmission coefficient for a plane wave multiplied by a term that changes the phase. In this permittivity estimation method, because the spot size at the beam waist in a Gaussian beam needs to be determined, we proposed an estimation method of the spot size by employing the measurement of the Line in Thru-Reflect-Line calibration; thus, no additional measurement is required. The permittivity estimation method was investigated for the E-band (60-90 GHz), and it was demonstrated that the relative permittivity of air with a thickness of 2mm and a sample with the relative permittivity of 2.05 and a thickness of 1mm is estimated with errors less than ±0.5% and ±0.2%, respectively. Moreover, in measuring a sample without displacing the receiving horn antenna to avoid the error in measurement, we derived an expression of the permittivity estimation for S parameters measured using a vector network analyzer, and demonstrated that the measurement of a sample without antenna displacement is valid.