A type of spatial modulating micro Fourier transform spectrometer (FTS) based on micro multi-step mirrors (MMSMs) is designed and manufactured in this paper. The interference system is based on Michelson interferometer, using two MMSMs instead of plane mirrors in two arms. The recovered spectrum is simulated with different distances between MMSMs and the detector, and the influence of diffraction on the recovered spectrum is analyzed. The edge-enlarging method for the MMSMs is proposed to eliminate edge noise, and the influence of surface roughness of MMSMs on the recovered spectrum is also analyzed. Moreover, the way of manufacturing the MMSMs is investigated.