A method of transforming high-order Gaussian beams (GBs) mode into circular symmetry fundamental Gaussian beam (FGB) mode with arbitrary waist size is presented using irradiance moments method in quasi-optical (QO) mode converters. The double shaped mirrors correcting amplitude and phase simultaneously are generated by a single incidence irradiance sampling data and known ideal output FGB taking advantage of linear moment matching technique and Fresnel diffraction theory, which can be applied to a wide frequency range especially significant for terahertz band. The numerical coding procedure of creating double correcting mirrors and its fast convergence speed are discussed at 325 GHz. Numerical and experimental comparisons reveal the conclusion that enhancing surface precision and increasing moments order can improve main lobe levels.