Infrared imaging spectrometers detect and identify targets by collecting spectral and image information. However, when detecting small temperature differences and dynamic targets, the accuracy of infrared detection is reduced, the traditional scanning structure detection time is longer, the real-time performance is poor and it is easy to introduce motion artifacts. This paper proposes an infrared polarization snapshot spectral imaging system (PSIFTIS) based on a polarizer array, a lens array and a roof-shaped stepped micromirror. Polarized light can solve the problem of small-temperature-difference target recognition by characterizing the surface properties of materials. Lens arrays utilize multi-aperture imaging to achieve snapshot detection of targets. The system can obtain 4D data information, including polarization, in a single measurement cycle. This study completed the overall optical design of a PSIFTIS and an optical simulation experiment using it. Finally, a system prototype was built in the laboratory and a polarization spectrum detection experiment was carried out. The experimental results show that the PSIFTIS could accurately obtain the polarization spectrum information for the target, the spectral resolution reached 7.8 cm⁻¹ and the Stokes measurement error was less than 5%.