AbstractNon-local thermodynamic equilibrium (NLTE) line formation for neutral and singly-ionized iron is considered through a range of stellar parameters characteristic of cool stars. A comprehensive model atom for Fe I and Fe II is presented. Our NLTE calculations support the earlier conclusions that the statistical equilibrium (SE) of Fe I shows an underpopulation of Fe I terms. However, the inclusion of the predicted high-excitation levels of Fe I in our model atom leads to a substantial decrease in the departures from LTE. As a test and first application of the Fe I/II model atom, iron abundances are determined for the Sun and four selected stars with well determined stellar parameters and high-quality observed spectra. Within the error bars, lines of Fe I and Fe II give consistent abundances for the Sun and two metal-poor stars when inelastic collisions with hydrogen atoms are taken into account in the SE calculations. For the close-to-solar metallicity stars Procyon and β Vir, the difference (Fe II - Fe I) is about 0.1 dex independent of the line formation model, either NLTE or LTE. We evaluate the influence of departures from LTE on Fe abundance and surface gravity determination for cool stars.