The electronic energy-band structure of the PrBaCo 2 O 5 + δ cobaltite at the oxygen content close to 5.5 are calculated by the first-principle PAW methods. The semiconductor–metal phase transition at 5 + δ = 5.5 is shown to be a result of the transition of cobalt atoms in the octahedral environment from the high-spin to low-spin state. The cause of the appearance of the metallic conduction is an increase in the energy of antibonding e g states of pyramidal cobalt atoms, and, as a result, they are at the Fermi level, thereby determining the metallic character of the system. The effect of a deviation of the oxygen content from 5.5 on the energy-band structure and the conductivity is studied. The semiconductor–metal transition is shown can be observed only in a narrow range of the values of 5 + δ lower 5.5.