In this study, the structures of two ultrathin Pd nanowires were predicted by the simulated annealing basin-hopping method (SABH) with the tight-binding potential. The thermal stability of the Pd wires and adsorption, dissociation and diffusion behaviors were further examined by the density functional theory (DFT) calculation and DFT molecular dynamics (DFT-MD) simulation. In terms of thermal stability, these two Pd nanowires are still very stable at temperatures as high as 400 K. The configurations and adsorption energy have been calculated for H atom and H2 molecular adsorption on Pd nanowires. The minimum energy pathways and transition states of H2 molecular dissociation and H atom diffusion process on Pd nanowires were studied by the nudged elastic band (NEB) method. For the dissociation of hydrogen molecules, results show the dissociation is almost barrierless so the dissociation is easy to occur at very low temperatures, and their catalytic reactivity is very similar to the Pd bulk material. The thermal stability of the H atom within these Pd nanowires were also investigated by DFT-MD, with results showing that the H atom can only stay within Pd nanowires at temperatures much lower than room temperature (298 K). This phenomenon is very different from that of H atoms within Pd bulk material or other reported nanomaterials, leading to hydrogen embrittlement. Our results reveal that these two ultrathin Pd nanowires not only possess the same excellent catalytic activity for hydrogen molecules as the bulk Pd materials or other Pd nanomaterials do, but also avoid the hydrogen embrittlement occur.