We developed a mid-infrared spectroscopy system with high spectral resolution and a high signal-to-noise ratio using an extremely high-order germanium immersion grating. The spectroscopic system covers wavelengths from 3 to 5 µm and has a spectral resolution of 1 GHz with a single-shot bandwidth of 2 THz. We proposed a method of improving the signal-to-noise ratio and achieved a ratio of over 3000 with a data acquisition rate of 125 Hz in the presence of fluctuations in the light source and environment. A signal-to-noise ratio of 10,000 was achieved with 0.1-s integration for 100-µW mid-infrared light.