The spin states of Co atoms in PrBaCo2O5 + δ with regard to the paramagnetic contribution of Pr3+ ions have been determined from magnetic property studies for δ = 0.52 and 0.74. Results obtained without considering the paramagnetic contribution of Pr3+ ions are inconsistent with available experimental data. With a decrease in temperature, the metal–insulator transition in PrBaCo2O5.52 becomes sharper according to a sharp change in spin states (from HS/LS to LS/IS) of Co3+ ions. In this case, Co3+ ions occupying octahedra pass from the high-spin state (HS, S = 2) to the low-spin one (LS, S = 0) and those occupying pyramids pass from the LS-state to the intermediate spin state (IS, S = 1), as follows from the available structural data. In PrBaCo2O5.74, the metal–semiconductor transition occurs smoothly from HS/LS to the HS/IS state upon the smooth transition of the Co3+ ion state from (LS, S = 0) to the (IS, S = 1) state in pyramides without change in the spin state of ions Co3+ (HS, S = 2) and Co4+ (LS, S = 1/2) in octahedrons.