We will present a design of high brightness light source for EUV lithography mask inspection. The required system parameters are minimum brightness of 2500W/mm2/Sr at 13.5nm/2% bandwidth. Our design consists of superconducting DC RF-gun as a radiator and 10.74nm CO2 laser stacked in an optical cavity as a laser undulator. Recent achievements of each component technologies, which is 1.3GHz SC-RF-gun, 10kW average power short pulse CO2 laser, and laser storage optical super-cavity, indicate the feasibility of producing required brightness based on laser Compton undulator. Design parameters of high brightness EUV source, the technological gap of the present component technologies and required further developments will be resented at the conference.