Brownmillerite(Ca2Al2O5-Ca2Fe2O5 solid solution) structure can be regarded as an oxygen-ion deficient perovskite structure. Because of high proportion of the oxygen vacancies in the structure, this material could be a candidate of fast oxide-ion conductor. Goodenough et al. indeed observed a first-order transition to a fast oxide-ion conductor at 930° C for Ba2In2O5 which adapts brownmillerite structure at ambient temperature. Molecular dynamics simulation was employed to study oxygen ion diffusion and phase transition of Ba2In2O5. The structure was well simulated at 300 K. When the system was heated, the original orthogonal cell transformed to a tetragonal cell at 2300 K. Inspection of the structure revealed that oxygen ions started to migrate from their original sites to nearest vacant oxygen sites at this temperature. The diffusion was restricted for the oxygen sites around In-tetrahedron, resulting highly anisotropie diffusion on the ac plane. At 4600 K it further transformed to an oxygen vacancies-disordered cubic perovskite structure. Although predicted transition temperature were apparently overestimated, the transition way to the phases with high oxygen ion diffusivity is consistent with the experimental results from electrical conductivity measurements. The high temperature cubic phase shows large ion conductivity. It is of interest to examine whether or not the cubic phase stabilizes in the low temperature region by making solid solution of another elements. We found that the cubic phase is stabilized below 500° C without any decrease of conductivity in BaIn1.9Ce0.1Oy and Ba2In1.8Nb0.2O5.