The proton exchange membrane plays a critical role as an electrolyte for proton transports in the PEMFC. Generally, the membrane, such as Nafion 117, consists of a polytetrafluoroethylene (PTFE) backbone and side-chains terminated with a sulfonate group (SO3-). Operating the fuel cell, the membrane preferentially becomes hydrated by absorbing water. Then, the hydrogen atom on the SO3- part of the side-chain can detach from its own position and hop to the next SO3- site. The water management is the key to the efficient operation of the fuel cell, since the water content is the one of decisive factors for membrane's lifetime and efficient operations of fuel cells as well. In this report, we set up the molecular model for hydrated Nafion 117 and simulate the molecular movements for various temperatures and monomer numbers. Here, we obtain the mean square displacements of water molecules and estimate the self-diffusion coefficients of water in the Nafion 117.