Optical system is the key to the miniaturization of spectrometer, which directly affects the performance and accuracy of a miniature spectrometer. After comparing different optical systems, a miniature long-wave infrared grating spectrometer based on cross-asymmetric Czerny-Turner structure is proposed for the purpose of long-wave infrared spectrum detection. First, based on the principle of spectrometer and the theory of optical design, the spectrometer’s spectral resolution, aberration, and detection sensitivity are studied. Then the optical system is optimized for goals of small size, low cost, required spectral range and resolution. Finally, the optical system is simulated in Zemax software. The results show that the spectrometer’s spectral range is 8～14 μm, and the spectral resolution is better than 80 nm, and the volume of the optical system is approximately 100 mm×75 mm×45 mm, which satisfies the requirements of miniaturization. A scanning grating and signal cooled detector are used to reduce costs.