Using the infrared thermopile array in the system as light receiver, with miniaturization and meet the requirements of certain spectral working range and spectral resolution as the system design task, according to the theory of spectrometer and the aberration, a mid-infrared plane grating spectrometer based on the structure of Czerny-Turner was designed. A double off-axis parabolic reflector was used as the fore-optical system to reduce the size of other optical elements, the toroidal focusing mirror was adopted to correct astigmatism. The ZEMAX software was applied to design, optimize and analyze the fore-optical system, imaging system of the spectrometer. Final analysis results show that the spectrometer system working range from 8.04 μm to 13.96 μm, spectral resolution is better than 80 nm, F number is 2, optical size of the system is 150 mm×200 mm×70 mm, and satisfy the design task.