The behaviors of hydrogen (H) adsorbed on the palladium (Pd) nanoparticles (NPs) are examined with the modified analytic embedded-atom method potentials and MORSE potentials. We study the effects of particle size and H coverage, and compare their adsorption properties of nanoparticle's facets with that of flat surfaces. We simulate the Pd truncated octahedron NPs with atoms from 38 to 2406 and the coverage of adsorbed H up to 1.0 monolayer (ML). Site preferences, adsorption geometries, adsorption energies, and bond lengths of H-Pd are calculated. We have also calculated the potential energy surface (PES). It is clear that the H atom binding to particle facets is quite stronger than that of flat surfaces when the particle size is smaller than 3.2 nm. We have found a significant variation that adsorption energies ascend gradually with increasing the particle size or surface coverage of H, and the adsorption energy varies about 0.6 eV for (111) facet and 0.3 eV for (100) facet as the coverage up to 1.0 ML. Our results are in reasonable agreement with the experimental values and other calculations.