The adsorption of water on Pt(111) surface has been studied with ab initio molecular dynamics simulation. Both the energetics and vibrational dynamics indicate the existence of a well-ordered molecular bilayer on this surface. This conclusion is in contrast to the recent result of water on Ru(0001) surface, but agrees with available experiments. In addition, our calculation identifies two different hydrogen bonds in the bilayer. Both can be directly recognized from the vibrational spectra of the OH stretch modes.