The invention provides a translational grating light valve Fourier spectrometer, in which an MEMS technology, a spectrum analysis technology and a Fourier digital transform technology are used; a system comprises a light source, an imaging system, a programmable spatial light modulator array and a single detector; a wave surface from a laser wave surface to a modulator is divided, a portion of light is reflected from an upper surface while the other portion of light is reflected from a lower surface, and the two light beams are coherent light and interfere with each other; the altitude difference between the upper surface and the lower surface of the programmable spatial light modulator can be changed by electrostatic actuation, sequentially, the optical path difference of the coherent light is changed, and interference fringe modulation is implemented; the change of light energy is detected by the single detector, sample information is measured by the Fourier digital transform technology and an optical path difference correction technology; and a conventional light-splitting grating or ion beam splitter is unnecessary, a single device has the dual function of light splitting and gating, the system is simplified, and the light path is shortened, so that the spectrometer is more compact in structure and high in integrated level, and can be widely used in various production researches.