An acousto-optic tunable filter (AOTF) is a new type of mono-wavelength generator, and an AOTF imaging spectrometer can obtain spectral images of interest. However, due to the limitation of AOTF aperture and acceptance angle, the light passing through the AOTF imaging spectrometer is weak, especially in the short-wave infrared (SWIR) region. In weak light conditions, the noise of a non-deep cooling mercury cadmium telluride (MCT) detector is high compared to the camera response. Thus, effective spectral images cannot be obtained. In this study, the single-pixel imaging (SPI) technique was applied to the AOTF imaging spectrometer, which can obtain spectral images due to the short-focus lens that collects light into a small area. In our experiment, we proved that the irradiance of a short-focus system is much higher than that of a long-focus system in relation to the AOTF imaging spectrometer. Then, an SPI experimental setup was built to obtain spectral images in which traditional systems cannot obtain. This work provides an efficient way to detect spectral images from 1000 to 2200 nm.