We have investigated the transport phenomena of hydronium ions and water molecules in the nanostructure of hydrated Nafion membrane by systematically changing the hydration level using classical molecular dynamics simulations. The new empirical valence bond (EVB) model is developed in order to improve the description of proton mobility in both aqueous and Nafion environments. The new EVB model predicts a significantly enhanced transport in comparison with previous hopping models as well as the classical hydronium diffusion, which largely improves the agreement with the available experimental data. We have determined diffusion coefficients of hydronium ions and water molecules in hydrated Nafion membrane as a function of hydration level to investigate the impact of the Grotthuss mechanism on the proton transport property. Proton hopping mechanism was found to become more significant at higher hydration levels.