The ferromagnetic phase transition and perpendicular magnetic anisotropy in one to eight monolayer fcc iron films are studied by the Green-function method based upon the Heisenberg model with perpendicular spin orientation of the atoms at the surfaces. The model calculation shows that the order parameter(spontaneous magnetizaton) changes with the atomic planes in the ferromagnetic films but the Curie temperatures of the atomic planes are all the same. We also calculate the surface anisotropy constant K s(T)

the effective volume anisotropy constant K v(T) and the shape anisotropy constant ( K v(T)-K d(T) >0) for an intermediate range of thickness of ultrathin films and temperature and prove that seven monolayer fcc iron film still has perpendicular remanence which agrees with the experiments for the ultrathin films of fcc Fe on Cu(001).