A novel optical resonator is proposed, so called unstable-stable coupling resonator, whose central portion acts as unstable resonator and edge portion acts approximately as stable resonator. Using Fox-Li method, the fundamental transverse modes of unstable-stable coupling resonator are computed. An optimization of the unstable-stable coupling resonator is given for a sealed-off CO2 laser with length of 1.2 m. Results show that output power of fundamental transverse mode can be increased about 2 times and central core output power on the focus plane can be increased about 1.5 times in comparison to stable resonators. And a design of unstable-stable coupling resonator is presented, which consists of a plat mirror, a spherical lens with aberration and a spherical mirror with aberration.