A small ultraviolet telescope which can be established on a satellite of the Korean small satellite (KITSAT) series is proposed with a concept design. Possible scientific objectives are identified, and the basic structure and characteristics of the telescope are described. In order to overcome limitation of pointing and stabilization accuracy of the KITSAT, a system of secondary stabilization is designed at the focal plane, where both star-tracking CCD and science detector share a 1.2deg field of view. Star tracking information is fed to three-axis drivers that move the platform on which the star-tracking CCD and science detector are installed. The proposed stabilization system is light and efficient, in comparison with a standard system of stabilization that basically moves the whole telescope or satellite. With a good intensified CCD and second stabilization system, the telescope will achieve a limiting magnitude of 21 at 1600 angstrom, which is sufficient for observing a variety of celestial objects, such as hot stars, nebulae, galaxies with UV excess, and quasars.