A fast method is offered for calculation of Voight spectral absorption line contour. A line profile is represented by a sum of terms of an absolutely converging series, containing undimensioned parameters a and b, connected with a property of the absorbing molecule, atmospheric temperature and pressure. The value b changes in a large limit from zero at the line center to 1000 and more at far wing of the line. The value a, describing a ratio of the Lorenz and Doppler effects, changes from a value ~5 near the surface of the Earth to 10-5 in the stratosphere. Twenty terms of series ensure the high accuracy of the approximation for values b ranging from 0 to 5. The deviation from accurate Voight contour formula is less than 4*10-4 or 0.04%. However, a large b value implies increase the number of terms, and the computing time increases accordingly. Numerical integration of Voight formula by Gauss-Hermite quadrature is simple, fast and accurate calculation for a value b> 5. In this case the deviation from accurate Voight formula is less than 2*10-5 or 0.002%. Using the proposed approximation of the Voight profile line, the atmospheric transmission function was computed for the path Sun- satellite represented as a net of tangent heights relative to the Earth’s surface up to 100 km with 1 km step. The computation method involves 29 spectral channels of the water absorption region (933-959 nm) and 14 channels of the molecular oxygen absorption region (758-771 nm). The computations were performed for certain profiles of H2O, O2, temperature and pressure. The computations results were compared with experimental data.