This paper introduces the "delta-Eddington" approximation, a method for calculating monochromatic radiative fluxes in absorbing-scattering atmospheres. The approximation combines a Dirac delta function and a two-term expansion of the phase function to overcome the limitations of the Eddington approximation for highly asymmetric phase functions. The fraction of scattering into the truncated forward peak is proportional to the square of the phase function asymmetry factor. Comparisons with more exact calculations show that the delta-Eddington approximation is accurate within 0.02 and has maximum differences of 0.15 over wide ranges of optical depth, sun angle, surface albedo, single-scattering albedo, and phase function asymmetry factor. The average error in fluxes is no more than 0.5%, and the maximum error is no more than 2% of the incident flux. This computationally fast and accurate approximation is useful in applications such as general circulation and climate modeling. The paper also discusses the errors in the delta-Eddington approximation, which are generally small and decrease with increasing asymmetry factor. The authors provide computer codes for monochromatic n-layer cases and suggest that vertical inhomogeneity can be treated by concatenating homogeneous layers.This paper introduces the "delta-Eddington" approximation, a method for calculating monochromatic radiative fluxes in absorbing-scattering atmospheres. The approximation combines a Dirac delta function and a two-term expansion of the phase function to overcome the limitations of the Eddington approximation for highly asymmetric phase functions. The fraction of scattering into the truncated forward peak is proportional to the square of the phase function asymmetry factor. Comparisons with more exact calculations show that the delta-Eddington approximation is accurate within 0.02 and has maximum differences of 0.15 over wide ranges of optical depth, sun angle, surface albedo, single-scattering albedo, and phase function asymmetry factor. The average error in fluxes is no more than 0.5%, and the maximum error is no more than 2% of the incident flux. This computationally fast and accurate approximation is useful in applications such as general circulation and climate modeling. The paper also discusses the errors in the delta-Eddington approximation, which are generally small and decrease with increasing asymmetry factor. The authors provide computer codes for monochromatic n-layer cases and suggest that vertical inhomogeneity can be treated by concatenating homogeneous layers.