The design of a novel low-background spectrometer based on lamellar grating interferometer (LGI) is presented. Reducing background noise helps to improve the spectrometer system detectivity for detectors operating under background limited performance (BLIP) regime, and then improve the signal to noise ratio (SNR) of spectrometer. The principle is that perfect mirrors do not emit blackbody radiation since their emissivity equals zero. Therefore, a lamellar grating interferometer based on a “cold” source and a “cold” detector becomes an extremely sensitive instrument because of the reduction of background radiation. Theoretical analysis shows that the system detectivity can be improved substantially with background radiation dropping. In ideal case, for a typical HgCdTe detector, the real BLIP detectivity obtained and corresponding SNR can be improved by three orders of magnitudes when background radiation is reduced from 300 K to 77 K. Besides, without cooling the interferometer, this configuration is more compact and easier-to-build compared with previously reported low-background Michelson spectrometer. This design has important significance for infrared sensitive detection.