We study the Eley-Rideal recombination of H atoms on graphene under the physical conditions of the interstellar medium. Effects of the ZPE motions of the chemisorbed H atom and of the graphene thermal motions are investigated. Classical molecular dynamics calculations undertaken with the multidimensional potential of Bachellerie et al. [Phys. Chem. Chem. Phys. 11 (2009) 2715] are reported. The ZPE effects are the strongest. The closer the collision energy is to the classical reaction threshold the more sizeable the effects. The quantum reaction cross section is also estimated below and above the classical threshold using a capture model. (C) 2010 Elsevier B.V. All rights reserved.