The diffusion of simple adsorbates on transition-metal stepped surfaces and nanoparticles is systematically studied using periodic, self-consistent density functional theory (DFT). The correlation between (a) the diffusion barrier on the terrace and that cross the step-edge of selected stepped surfaces and nanoparticles and (b) the binding energy of different adsorbed species is examined. We show that there is a good correlation between the diffusion barrier and the binding energy of the adsorbed species on the terrace. By contrast, the correlation between diffusion barrier cross the step-edge and the binding energy of the adsorbates is weak. Our findings could be of importance for catalytic reactions on transition-metal stepped surfaces and metal nanoparticles.