In this study, in order to identify the effect of surface coverage and structure over Co catalyst on the behaviors of H-2 adsorption and activation, the adsorption, dissociation and desorption of H-2 at different coverage over the periodic p(3 x 3) Co(0001) and (100) surfaces have been examined over Co catalyst, in which H-2 adsorption with the parallel and vertical modes at different sites have been considered. Here, the results are obtained using density functional theory calculations. Our results that H-2 adsorption from low to high coverage at the hollow sites over Co surfaces dominantly focus on the dissociative adsorption. Meanwhile, only H-2 adsorption with the parallel mode at the top site is the molecular adsorption, which correspond to the saturated coverage of 4/9 and 7/9 ML over Co(0001) and (100) surfaces, respectively; moreover, the dissociations of these molecular adsorption H-2 are much more easier to occur rather than their desorption. As a result, H2 dissociative adsorption and the dissociation of molecular adsorption H2 over Co(0001) and (100) surfaces are independent of its surface coverage and structure, namely, when there are the continuous supplies of H-2 in syngas conversion, H2 will exist in the form of the dissociative H atoms from low to high coverage over Co surfaces under the realistic condition. Therefore, Co surfaces exhibit good catalytic activity towards the adsorption, activation and dissociations of H-2. Our results give out the reasonable explanations for many catalytic systems related to H-2 on Co surfaces, in which all studies related to H2 are in the form of H atoms rather than H-2 molecule. (C) 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.