Hydrogen dissociative chemisorption and desorption on small lowest energy Ni(n) clusters up to n=13 as a function of H coverage was studied using density functional theory. H adsorption on the clusters was found to be preferentially at edge sites followed by 3-fold hollow sites and on-top sites. The minimum energy path calculations suggest that H(2) dissociative chemisorption is both thermodynamically and kinetically favorable and the H atoms on the clusters are mobile. Calculations on the sequential H(2) dissociative chemisorption on the clusters indicate that the edge sites are populated first and subsequently several on-top sites and hollow sites are also occupied upon full cluster saturation. In all cases, the average hydrogen capacity on Ni(n) clusters is similar to that of Pd(n) clusters but considerably smaller than that of Pt(n) clusters. Comparison of hydrogen dissociative chemisorption energies and H desorption energies at full H-coverage among the Ni family clusters was made.