  A comprehensive model atom for Fe with more than 3000 energy levels is
presented. As a test and first application of this model atom, Fe abundances
are determined for the Sun and five stars with well determined stellar
parameters and high-quality observed spectra. Non-LTE leads to systematically
depleted total absorption in the Fe I lines and to positive abundance
corrections in agreement with the previous studies, however, the magnitude of
non-LTE effect is smaller compared to the earlier results. Non-LTE corrections
do not exceed 0.1 dex for the solar metallicity and mildly metal-deficient
stars, and they vary within 0.21 dex and 0.35 dex in the very metal-poor stars
HD 84937 and HD 122563, respectively, depending on the assumed efficiency of
collisions with hydrogen atoms. Based on the analysis of the Fe I/Fe II
ionization equilibrium in these two stars, we recommend to apply the Drawin
formalism in non-LTE studies of Fe with a scaling factor of 0.1. For the Fe II
lines, non-LTE corrections do not exceed 0.01 dex in absolute value. The solar
non-LTE abundance obtained from 54 Fe I lines is 7.56+-0.09 and the abundance
from 18 Fe II lines varies between 7.41+-0.11 and 7.56+-0.05 depending on the
source of the gf-values. Thus, gf-values available for the iron lines are not
accurate enough to pursue high-accuracy absolute abundance determinations.
Lines of Fe I give, on average, a 0.1 dex lower abundance compared to those of
Fe II lines for HD 61421 and HD 102870, even when applying a differential
analysis relative to the Sun. A disparity between Fe I and Fe II points to
problems of stellar atmosphere modelling or/and effective temperature
determination.
