The interpretation of infrared radiance measurements made by satellite-borne limb-scanning broadband radiometers requires accurate and computationally fast techniques with which to evaluate the equation of radiative transfer. This requirement is made even more stringent when analyzing measurements of non-local thermodynamic equilibrium (non-LTE) emission from the terrestrial mesosphere and lower thermosphere. In principle, line-by-line calculations which explicitly account for the departure from thermodynamic equilibrium in both the source functions and the transmittances are necessary. In this paper we extend the emissivity growth approximation (EGA) technique developed for local termodynamic equilibrium (LTE) conditions to the non-LTE environment. Computations of the non-LTE spectrally integrated limb radiance for the molecular oxygen dayglow (1.27 μm and 762 nm), ozone and carbon dioxide in the 9- to 11-μm spectral interval, carbon monoxide (4.6 μm), nitric oxide (5.3 μm), and the carbon dioxide bands (15 μm) are presented. Using the non-LTE form of the EGA, the spectrally integrated limb emission is calculated for 35 tangent heights in the mesosphere and lower thermosphere (a total of 1200 atmospheric layers) with line-by-line accuracy in ~0.35 s of CPU time on readily available desktop computer hardware, while the corresponding line-by-line calculations may require several minutes. The non-LTE EGA technique will allow kinetic temperature and minor constituent retrieval algorithms to readily include non-LTE effects limited only by the a priori knowledge of the departure from LTE in the observed bands.