We propose a microscopic diffusion mechanism of protons and Na+ ions in phosphate glasses using first-principles molecular dynamic simulations. Protons hop and are chemisorbed onto non-bridging oxygen (NBO) of nearby PO4 tetrahedra through hydrogen bonds. The subsequent behavior depends on the morphology of the PO4 tetrahedra (QnP values). When a proton is adsorbed onto the NBO of a Q3P unit, it is desorbed on a short time scale of within 10 fs and re-adsorbed onto the NBO that was previously adsorbed. However, when a proton is adsorbed onto the NBO of a Q2P unit, another proton coordinated before adsorption is desorbed in a chain, resulting in the diffusion of protons. When a Na+ ion is present in the vicinity, the adsorption of a proton onto a Q2P unit leads to a decrease in the electrostatic interaction between Na+ and O- ions and induces the diffusion of Na+ ions. We conclude that the difference in the morphology of PO4 tetrahedra greatly affects the diffusion of protons and Na+ ions.