The internal structures as well as adsorption and hopping energies of monomers, dimers, trimers, tetramers, pentamers and hexamers of water on Pd(111) have been studied by density functional theory (DFT) plane-wave pseudopotential method which performs the first- principles quantum-mechanical calculations to explore the properties of crystals and surfaces in materials. Based on the calculations, we suppose that their absorption is via one water molecule for monomers, dimmers and trimers, but three water molecules for pentamers and hexamers. Moreover, there is one water molecule bonding with Pd atom by O atom in pentamers and hexamers, which explains why pentamers and hexamers are stable. The binding energies of polymers may be used to explain why the trimer comes close to two nearby monomers to form a stable pentamer instead of tetramer. And the difference of mobility of small water clusters is due to their different hopping energies. The internal structures as well as adsorption and hopping energies of monomers, dimers, trimers, tetramers, pentamers and hexamers of water on Pd (111) have been studied by density functional theory (DFT) plane-wave pseudopotential method which perform the first- principles based on the calculations, we suppose that their absorption is via one water molecule for monomers, dimmers and trimers, but three water molecules for pentamers and hexamers. Moreover, there is there is one water molecule bonding with Pd atom by O atom in pentamers and hexamers, which results why pentamers and hexamers are stable. The binding energies of polymers may be used to explain why the trimer comes close to two nearby monomers to form a stable pentamer instead of And the difference of mobility of small water clusters is due to their different hopping energies.