We numerically investigate the Josephson transport through ferromagnetic insulators (FIs) by taking into account its band structure. By use of the recursive Green's function method, we found the formation of the π junction in the case of the fully spin-polarized FI (FPFI), e.g., La2BaCuO5. Moreover, the 0-π transition is induced by increasing the thickness of FPFI. On the other hand, Josephson current through the Eu chalcogenides shows the π junction behavior in the case of the strong d-f hybridization between the conduction d and the localized f electrons of Eu. Such FI-based Josephson junctions may becomes a element in the architecture of future quantum information devices.