The influence of dielectronic recombination (DR) of projectile ions on characteristics of fast heavy-ion beams passing through cold plasmas is studied on the basis of fully relativistic multi-configuration calculations of DR rate coefficients. Present results are compared with the first (and, to our knowledge, the only ones) results for DR rates of 1.5-MeV/u iodine ions penetrating fully ionized hydrogen plasma with the electron temperature Te = 10 eV and density Ne = 1020 cm−3 calculated in the hydrogenic approximation (Th. Peter and J. Meyer-ter-Vehn, Phys. Rev. A 43, 2015 (1991)). Confirming the importance of DR processes of ions moving through plasma, our calculations give much higher DR-rate values than those calculated by Th. Peter and J. Meyer-ter-Vehn, which significantly changes the non-equilibrium and equilibrium ion charge-state fractions, the mean and equilibrium charges of projectile ions, as well as the equilibrium thickness of hydrogen plasmas. In order to perform DR-rate calculations for arbitrary ions passing through plasma, a new computer code DRIMP (Dielectronic Recombination of Ions Moving in Plasmas) is developed and described in the paper.