A molecular dynamics simulation model has been developed and used to investigate the microscopic transport mechanism and various physical properties in an electrolyte for polymer electrolyte fuel cells. It has successfully reproduced experimental results of diffusion coefficients of positive ions and water molecules in the polymer electrolyte, which are one order of magnitude smaller than those in aqueous solutions, and of O-H vibration spectra having higher frequencies than in liquid water. The low diffusivity in the polymer electrolyte is due to polar particles forming a disordered heterogeneous structure of the hydrophilic region, which constitutes the transport paths for ions and water molecules. About 25% of the positive ions are dissociated from sulfonate anions at the ends of side chains in the hydrated electrolyte and move sequentially from one sulfonate anion to the other in the vicinity of 0.5 nm about two or three times per nanosecond. This transport mechanism of ions means that the main constraining factors for ion transport in the polymer electrolyte are coulombic interactions from the sulfonate anions and tortuosity of the hydrophilic region. Based on the results, guiding principles to enhance ion diffusivity in the polymer electrolyte are proposed.