Density functional theory has been performed to investigate the interaction of H 2 and Pd n clusters (n=1–7). The local minima configurations for different H 2 molecule approach modes towards Pd n clusters are presented. Our results show that in some cases H 2 is physically adsorbed around Pd atom, and in other cases H 2 is dissociated to be H atoms. Except for PdH2, Pd n clusters with H atoms dissociatively adsorbed are most stable. For these most stable PdnH2 clusters (n⩾2), the binding energy of hydrogen atom decreases as the number of Pd atom increases until n=4, and when n⩾4, the binding energy almost keeps constant with the H atoms bound sites changing from Pd–Pd bonds to Pd triangle planes. Besides, the adsorption of H 2 on other low-lying isomers of Pd n clusters is also discussed.