As an important optical instrument, spectrograph is widely used to analyze material components and some characteristics through spectral analysis, such as chemical research, medial detection, food industry, geological detection and other fields. Different spectrographs shall be chosen in different application fields. In this study, a transmission spectrograph was designed to detect spectrum of light scattered on an object surface. Working distance of this spectrograph was 30 mm and a coaxial illumination system was used in this spectrograph. Such illumination scheme eliminates reflected light rays of the objective lens and specular reflection light rays on the testing object surface by using polarization beam splitter, which increases the accuracy of the instrument. A LED was applied as the lighting source, so the instrument is characterized by low power consumption, quick response, and long service life. The designed spectrograph is optimized generally by CODE V10.4 with appropriate initial parameters and aspherical lens. The detection range and spectral resolution of the spectrograph are 400-780 nm and 0.4 nm, respectively.