In order to meet the urgent requirements of detecting atmospheric trace gas in limb observation geometry, an optical system of spaceborne broadband limb sounder for detecting atmospheric trace gas is designed. The system is an imaging spectrometer with the working wavelength band from 0.3 μm to 0.7 μm, and its full field of view is 2.4°, focal length is 120 mm, and the relative aperture is 1∶6. To avoid the problems of the classical CzernyTruner spectrometer, such as low spatial resolution caused by large astigmatism, a modified CzernyTurner spectrometer is designed, in which astigmatism can be corrected simultaneously in a wide band. By matching the modified CzernyTurner spectrometer with a offaxis parabolic telescope，an example of limb sounder optical system is designed. Ray tracing, optimization and analysing are performed by ZEMAX software. The analyzed results demonstrate that the astigmatism is substantially corrected, and the MTF for different spectral band is more than 0.69, which satisfies the predesigned requirement and proves the feasibility of the astigmatismcorrection method.