We have performed an atomistic analysis of transport phenomena of hydronium ions and water molecules in the hydrated Nafion membrane. The new empirical valence bond (EVB) model is developed based on the previous study of EVB model reported by Walbran et al. in order to improve the description of proton mobility in both aqueous and Nafion environments. We have calculated mean square displacement (MSD) to determine diffusion coefficients of hydronium ions and water molecules as a function of hydration level for the investigation of the impact of Grotthuss mechanism on the transport property of solvent molecules as well as the validation of our simulation by comparing with the experimental data of diffusion coefficients. A large contribution of Grotthuss mechanism for the diffusion of hydronium ions has been found at high water contents, testifying the important impact of Grotthuss mechanism in the membrane as well as in the bulk aqueous solutions.