This paper presents a spatial modulation Fourier transform micro-spectrometer based on micro-optical elements. The infrared microstructure diffractive optical elements, multi-step micro-mirrors and microlens array are introduced to realize the miniaturization of the instrument. In addition, the structure and basic principle of Fourier transform infrared micro-spectrometer are introduced. The design theory of micro-collimation system is analyzed based on the negative dispersion, the abberation correction and the arbitrary phase modulation characteristics of diffractive optical element. Combined with the characteristics of micro-static interference system, the micro-focusing coupled optical system is analyzed and designed. Based on the wave aberration theory and the Sellmeier dispersion formula, the influence of residual aberration on spectral recovery and the diffraction efficiency of diffraction surface in single-chip hybrid diffractive-refractive collimating lens are studied. The effects of diffraction of multi-stage micro-mirrors and the aperture diffraction of microlens array on spectral recovery are studied by using the scalar diffraction theory. Furthermore, the influence of axial assembly error of relay system on the whole system performance is studied. The results show that the diffraction efficiency of the diffraction surface, the diffraction of the multistage micro-mirror and the microlens array have no effect on the recovery spectrum when the working band of the system is 3.7-4.8 μm. Finally, in order to verify the accuracy of the system design results, an optical simulation software is used to simulate the infrared micro-Fourier transform spectrum. The accuracy of the system model is verified by the simulation that the reconstructed spectrum is in agreement with the ideal spectral curve and the actual spectral recovery error is 2.89%. The medium-wave infrared micro-static Fourier transform spectrometer has no movable parts and adopts micro-optics element to replace the traditional infrared lens. Therefore, it has the advantages of not only good stability, but also small size and light weight so that it is helpful in on-line monitoring applications and provides a new design idea about the micro-Fourier transform spectrometer.