To meet the requirements of the solar mid-infrared spectral band CO 4.66-μm spectrum observations， a high-resolution mid-infrared spectrograph with a 4.667-μm central wavelength was designed. First， the technical indicators were studied based on the requirements of the scientific observations that have to be made. The entire spectrograph was put in a vacuum liquid-nitrogen refrigeration vessel to reduce the background radiation from the infrared equipment. An echelle is used in the spectrograph as a spectrum splitter to increase the observation resolution. The optical configuration of the spectrograph uses a creative structure by combining the Littrow structure and the Three-Mirror Anastigmatic （TMA） technology. Such a structure provides better imaging quality and optical path compression. In addition， the TMA structure has dual functions， as the collimating and imaging optical paths. The design and optimization methods of the coaxial three-mirror structure， TMA structure， and spectrograph structure were also studied based on the coaxial three-mirror system's geometrical optical imaging theory. The designed spectrograph has a size of less than 700 mm， a focal length of 1 300 mm， a numerical aperture of 0.035， and a field of view of 20.3'×0.158'. The imaging quality of the spectrograph system was evaluated， with results indicating that， within the working wavelength， the root-mean-square diameter of the spot diagram is less than 5 μm， and the energy focuses on one pixel. Therefore， the spectrograph meets the design requirements.