Based on a theoretical analysis, the optimum path and the diffusivity are proposed for the proton hopping in perovskite-type oxides (ex. Sc-doped SrTiO3), and the possible electric conduction paths and the diffusion constants are explained by comparing with some kinds of experimental data, Furthermore, numerical results suggest the possibility of a new conduction mechanism; the proton jumping process along the O-O bond at high-temperatures changes to proton tunneling process, leading to an almost T-independent conductivity at low temperatures. Within this theoretical approach in perovskite-oxides, the high-conduction mechanism with low proton concentration is discussed with reference to the results by MD simulation and the neutron diffraction, including the prediction on H(D)-isotope effect and the pressure dependence of the proton conductivity.