The magnetic anisotropy of Fe film grown on vicinal Ag(1,1,10) surfaces was studied with the in situ magneto-optic Kerr effect. Below 200 K, strong oscillations of the uniaxial magnetic anisotropy as a function of Fe thickness with a period of 5.7 monolayers are found, which can even cause the easy magnetization axis to oscillate between perpendicular and parallel to the steps. Such novel oscillation of the anisotropy is attributed to the quantum well states of d-band electrons at the Fermi level in the Fe film. This is unlike the previously observed oscillatory behaviors of ferromagnetic films caused by the quantum well states in nonmagnetic interfacing layers.