The theoretical analysis of oxygen-ion conductivity in double perovskite type oxides was performed. The model of ion transport was developed by considering two energetically non-equivalent oxygen positions for ion jumps in the crystalline structure. The temperature variations of oxygen ion conductivity were shown to depend on thermodynamic parameters of the intrinsic oxygen disordering process. The model proposed was verified by experimental data for perovskite-like non-stoichiometric PrBaCo2O6-delta, Sr3Fe2O7-delta and its titanium-doped derivative.