Hydrogen adsorption, desorption and dissociation on the Co(100), (311), (111) and (110) surfaces at different coverage have been systematically studied using density functional theory and ab initio atomistic thermodynamics. On the basis of the computed stepwise H-2 adsorption energies, the saturated coverage on the Co(311), (111), (110) surfaces are 8/18, 3/9 and 6/18 ML, respectively, revealing that these surfaces have different potential hydro treating abilities and activity. The lateral repulsive interactions can affect the adsorption structures and become stronger with the increasing of H-2 coverage, which lead to H-2 migration over Co surfaces. Comparison of dissociation energies and corresponding desorption energies, it can be concluded that H-2 molecules prefer dissociation rather than desorption both kinetically and thermodynamically at different coverage. Hydrogen stable coverage on the surfaces highly depends on temperatures and H-2 partial pressure. These results should provide important information about morphology of Co-catalysts under Fischer-Tropsch synthesis reduction conditions. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.