A novel static Fourier transform spectrometer (FTS) is proposed. The interference system of the spectrometer uses two micro mirrors with periodic structure to replace the plane mirrors in the Mach-Zehnder interference system, without any driving parts and generation of backtracking light, which realizes the static state and high optical flux of the FTS. In this paper, the working principle of static FTS is introduced, the Mach-Zehnder interference system model based on micro mirrors is established, and the interferogram and spectrogram in frequency domain of the interference system are obtained by simulation. Compared with the ideal results, the fringe contrast is reduced and the reduction in the edge area is more serious in the interferogram obtained by simulation, and the peak value of the main frequency is reduced and the baseline noise is obvious in the spectrogram in frequency domain obtained by simulation. The analysis shows that when the incident beam is inclined, the stepped periodic structure of two micro mirrors will not only cause the uneven energy distribution of the interference light field and the deviation of two coherent beams, but also cause the diffraction effect. The simulation results show that the distortion of information in interferogram can be effectively reduced by increasing the number of subreflectors of two micro mirrors and the length of subreflectors. Furthermore, the ideal spectrogram in frequency domain can be obtained by reducing the step interval between the subreflectors of the two micro mirrors under the premise of satisfying the performance of the spectrometer.