The short-wave infrared (SWIR) grating imaging spectrometer based on indium gallium arsenide (InGaAs) material inverts the atmospheric methane concentration by measuring the scattered light signals in the sky. This study proposes spectral and radiometric calibration methods for the characteristics of the spectrometer, such as the small-area array, high signal-to-noise ratio, and high spectral resolution. Four spectral response function models, namely, the Gauss, Lorentz, Voigt and super-Gaussian models, were compared during spectral calibration. With a fitting residual of 0.032, the Gauss model was found to be the most suitable spectral response function for the spectrometer. Based on the spectral response function, the spectral range and spectral resolution of the spectrometer were determined to be 1592.4-1677.2 and 0.1867 nm, respectively. In addition, radiometric calibration of the spectrometer was achieved by combining an integrating sphere and linear measuring instrument. Moreover, absolute and relative radiometric calibrations of the spectrometer were performed. The low signal response problem caused by the quantum efficiency of the detector at long wavelength was corrected, and the uncertainty and non-stability uncertainty of absolute radiometric calibration were calculated to be less than 0.2%. Finally, the calibrated spectrometer was used to accurately measure the solar scattering spectrum in the SWIR band, and the solar spectrum was simulated by the radiative transfer model for verification; the measurement error was found to be 5%. Concurrently, a methane sample gas experiment was performed using the integrating-sphere light source, and the measurement error was less than 4%. This fully proves the effectiveness of the spectral and radiometric calibrations of the SWIR spectrometer and strongly guarantees a subsequent, rapid and accurate inversion of atmospheric methane concentration.