The invention discloses a Fourier spectrometer based on a digital micromirror device. The spectrometer comprises a light source, a slit, a collimating lens I, a band pass filter, a diffraction grating, a focusing lens, a digital micromirror DMD chip, a collimating lens II, a mixing and focusing optical device set, a sample cell, a detector, an I / V switching amplifier, an analog to digital converter, a microprocessor and a liquid crystal display. A system of the spectrometer temporally and spatially modulates the detecting light source by using a DMD chip based on frequency division multiplexing, and then detects a sample to obtain a modulated light detecting signal, and finally demodulates the detecting signal by using the digital Fourier transform technology to obtain the complete spectrum of the sample. Compared with the traditional Fourier spectrometer, the spectrometer adopts the DMD chip to replace precision mechanical moving assemblies like the Michelson interferometer, thereby greatly increasing the reliability, reducing the cost and the instrument size and achieving the purpose of portability. The spectrometer has low requirements for use environments, the detection processis fast and accurate, and the signal to noise ratio is high.