The present paper puts forward a novel micro-Fourier transform infrared spectrometer based on programmable MEMS micro-mirror. This design uses a MEMS micro-mirror and a slantwise reflector to replace the moving mirror system on traditional spectrometer. This paper analyzes the operating principle of this spectrometer and gives the simulation result to prove the feasibility of this method. The results show that the spectral resolution is less than 5 nm in near-infrared wave band, the wavelength accuracy is approximately 1 nm and the sampling period of this spectrometer is approximately 50 ms. This method can use Hadamard transform to improve the SNR.