Density functional theory was used to investigate the effect of size on the adsorption state of hydrogen atom on small cobalt particles. For this propose, we have performed series of DFT-GGA calculations on various sizes of Co clusters, between 4 and 24 atoms, and a Co FCC (100) slab, with and without hydrogen atom adsorbate. The results showed that the destabilization and the cohesive energies per atom in a metal cluster are represented as linear function of the surface-to-volume ratio of the metal clusters. In addition, the energy of the HOMO–LUMO gap from 4s and 3d valence orbitals of the cobalt atoms in the cluster is decreased with increasing in cobalt cluster size, which is size dependent parameter. We have studied the effect of the size of Co clusters and the infinite Co (100) surface, on the energy of adsorption of hydrogen atom. The calculated Eads for hydrogen atom in our considered cobalt clusters showed decreasing behavior with increasing of the number of atoms in cluster.