We present a many-body interatomic potential for Pd within the second-moment approximation of the tight-binding model by fitting to the volume dependence of the total energy of the metal, computed by first-principles linearized augmented plane wave calculations. This potential achieved good accuracy for the elastic constants, phonon spectrum, along with the temperature dependence of the lattice constant of Pd. This was also used, in tandem with molecular-dynamics simulation, to study the self-diffusion of single adatoms on Pd(1 1 1) surface. The diffusion coefficient of Pd adatoms was computed, and was found to present Arrhenius behavior. The migration energy and pre-exponential factor for hopping mechanism were determined and compared with recent scanning tunneling microscopy measurements and previous calculations. Our computed values are generally in better agreement with the experimental data, than those of previous computational works.