First-principles room-temperature molecular dynamics (MD) simulations are conducted to investigate proton transfer (PT) in Na zeolites. The MD are performed on the unit cell containing two Al-sites, one of them saturated with H (acid site) and the second one with Na coordinated with three water molecules. The creation of the charged H3O+ cations is suppressed by the Na cation. Spontaneous barrierless PT between the O-sites in the zeolite, however, is possible. The lifetime of the hydronium cation is extremely short (less than or equal to5 fs). The presence of Na+ cations leads to a modified mechanism but does not suppress the proton transfer around the Al-site in zeolites.