An accurate but computationally fast scheme of the infrared radiative transfer is developed based upon the multiparameter random model to be used in climate and numerical prediction models. The entire infrared spectrum is divided into four spectral regions, 20--550, 550--800, 800--1200, and 1200--2200 cm-1, including the H2O rotation and 6.3 μm bands, the CO2 10- and 15-μm band, and the O3 9.6- and 14-μm bands. The continuum absorption of H2O is incorporated in all the spectral regions. The mean diffuse transmittances in each region for homogeneous paths are calculated by a line-by-line method, and they are approximated with a simple exponential function which contains 10 or 12 parameters. The transmittance calculations through inhomogeneous atmosphere are carried out by the modified Godson method, which independently uses the Godson method to the line and wing parts of the transmission function. This method is found to be more economical in computation time than the current Godson method, keeping the same precision. The errors in heating rates calculated by this scheme for the model atmospheres are less than 0.3 K/d in the troposphere and stratosphere, and less than 0.8 K/d above the stratopause. The errors in radiative fluxes are less than 0.8 W/m2 both at the Earth's surface and the top of the atmophere. It is also shown that the accuracy of this scheme does not degrade when the CO2 concentration is doubled. It is pointed out that the inclusion of the H2O continuum in 20--550 cm-1, O3 14 μm in 550--800 cm-1, and CO2 10 μm in 800--1200 cm-1 significantly affects radiative flux and cooling rate. ¿ American Geophysical Union 1989