A new type of laser resonator with annular output beam is presented. Annular output beam is obtained by outer ring coupling in a stable laser resonator. The integral equation of this type of laser resonator is resolved by using Fox-Li numerical iteration method. Amplitude distributions and phase distributions of fundamental mode of the diffraction-coupling output field and the fields on the surfaces of the mirrors are computed by computer programming when the output plane mirror's radius varies in a plane-concave stable resonator. The theoretical results predict that there exists steady diffraction output field with annular beam distribution when the output plane mirror's radius is less than that of the fundamental mode in an usual stable resonator. Experimental TEA CO2 laser with printed circuit board preionization is used. The laser has gain length of 90 cm. The resonator is composed of a total-reflective concave spherical mirror of curvature radius 20 m and a total-reflective plane mirror of mirror radius 4.5 mm, separated by 5 m distance. The annular output spot of fundamental mode with inner radius 4.5 mm and outer radius 5.5 mm is obtained by the experiment. Therefore the feasibility of the scheme generating annular beam has been verified theoretically and experimentally.