The application of starlight refraction navigation to spacecraft and space weapons is a significant development direction. Observing enough refracted stars for the star sensor in a strong limb background is an urgent problem. The all-day optical system parameters are analyzed based on the star detection requirement and navigation accuracy. Combined with primary aberration theory, the prime-focus catadioptric optical system is selected to meet the design requirements of a wide field of view (FOV) and tight structure. An H-band (1.52um-1.78um) star sensor is designed with a FOV of 6°, a focal length of 831mm, an effective aperture of 253mm, and a relative distortion of 0.03%. The energy concentration of the star point is 85% within 30um, and the maximum lateral chromatic aberration is 2.9um, which meets the imaging requirements. Furthermore, a baffle is designed to avoid the influence of direct sunlight on stellar imaging. The proposed method can provide a theoretical foundation and technical support for the optical design of the refraction star navigation.