A fast radiative transfer model has been developed for simulating high-resolution absorption bands. The first scattering radiance is calculated accurately by using the higher number of layers and streams for all required wave number grids. The multiple-scattering component is extrapolated and/or interpolated from a finite set of calculations in the space of two integrated gaseous absorption optical depths to the wave number grids: a double-k approach. The double-k approach substantially reduces the error due to the uncorrelated nature of overlapped absorption lines. More importantly, these finite multiple-scattering radiances at specific k(λi) values are computed with a reduced number of layers and/or streams in the forward radiative transfer model. To simulate an oxygen A-band spectrum, 28 calculations of radiative transfer are needed to achieve an accuracy of 0.5% for most applications under all-sky conditions and 1.5% for the most challenging multiple-layer cloud systems (99% of spectrum below 0.5%). This represents a thousandfold time reduction in the standard forward radiative transfer calculation.