The ground-based airglow imaging interferometer (GBAII) observes the nighttime airglow of the O₂(0-1) 867.7 nm line, peaked at 94 km altitude, to measure the upper atmospheric wind and temperature field. Its forward model, a code package in interactive data language (IDL), is developed to simulate the expected imaging interference fringes. It includes eight modules to simulate the light source, the atmospheric radiation transmission, the wide-angle Michelson interferometer, the interference filter, the optical system decay function, the responsivity, the imaging CCD, and the noises. The inverse method is also developed for obtaining the rest phase calibration, temperature, and wind. By means of both theoretical tools, we carry out a comparison of theoretical results with a field observation case. The apparent quantities J(1-p) from the forward model has the deviation of 1.5%-2.5% compared with that from the observation image. The temperature falls mainly in the range of 167-196 K with the precision of 2 K. The zonal and meridional winds are mainly in the region of 5.1 to 46.5 m/s and 12.5 to 48.3 m/s respectively, with errors of 13.2 to 21.5 m/s. The consistent trends between the observation results and standard models (MSISE90 and HWM93) suggest that the forward model and inverse method are suitable for GBAII.