We construct infrared star-count models of the Galaxy, applicable at faint magnitudes, based on the models and luminosity functions (LFs) obtained at V. Two types of models are derived. First, we derive infrared versions of the disk and halo models by Gould et al., who obtained the local LFs and functional forms of the models based on Hubble Space Telescope (HST) star counts. Second, we construct a double exponential disk model based on the LF of nearby stars by Reid & Gizis and a halo model based on the nearby-subdwarf LF of Dahn et al. In addition to the dwarfs and subdwarfs included in the original models, we also take into account L dwarfs, T dwarfs, and white dwarfs of both disk and halo. As a test case for the models, we analyze the infrared imaging data at J and K' obtained during the Subaru Deep Field survey to study stellar objects. Out of about 350 objects, 14 stellar objects are selected in a 2' x 2' field based on a morphological criterion applied to the J-band image. Both the completeness and the contamination associated with the selection criterion are evaluated by simulations. The J-band image is 57% complete at J = 24, and the number of contaminants is estimated to be negligible. The prediction of the HST-based models agrees with the observed count at -0.8 sigma, and that of the nearby-star LF-based models also agrees with the observations at +1.0 sigma. The observed count is between the predictions of the two types of models, which have contradictory local LFs. With our limited statistics, the observational data do not favor a particular type of model. The infrared star-count models we have obtained predict that the Next Generation Space Telescope will see primarily T dwarfs, M subdwarfs, and old halo white dwarfs at faint magnitudes.