In order to evaluate the ground-based infrared telescope sensitivity affected by the noise from the atmosphere, instruments and detectors, we construct a sensitivity model that can calculate limiting magnitudes and signal-to-noise ratio (S/N). The model is tested with tentative measurements of M '-band sky brightness and atmospheric extinction obtained at the Ali and Daocheng sites. We find that the noise caused by an excellent scientific detector and instruments at -135 degrees C can be ignored compared to the M '-band sky background noise. Thus, when S/N = 3 and total exposure time is 1 second for 10 m telescopes, the magnitude limited by the atmosphere is 13.01(m) at Ali and 12.96(m) at Daocheng. Even under less-than-ideal circumstances, i.e., the readout noise of a deep cryogenic detector is less than 200e(-) and the instruments are cooled to below -87.2 degrees C, the above magnitudes decrease by 0.056(m) at most. Therefore, according to observational requirements with a large telescope in a given infrared band, astronomers can use this sensitivity model as a tool for guiding site surveys, detector selection and instrumental thermal-control.