The expression of the M2 factor of the beam generated by Gaussian mirror resonator is derived based on the two-order matrix method, and the effects of the peak reflectivity value and the radius of the light spot on the film of the Gaussian mirror on the M2 factor are explored. The curves of the M2 factor are plotted with different peak reflectivity values and the radii of the light spot on the film. Integrating the whole beams from the Gaussian mirror resonator, the propagation property of the beam through an ABCD system with the diaphragm effect neglected is discussed, based on scalar diffraction theory and matrix optics theory. The curve of normalized optical intensity distribution versus different positions in free-space propagation is plotted.