By controlling the polarization of synchrotron radiation with a linear polarizer and a phase plate, the magnetic effect in non-resonant x-ray magnetic diffraction from a ferromagnet was enhanced for the first time. A silicon double-crystal monochromator, the Bragg angle of which was close to , was used as the linear polarizer and a diamond single-crystal was used as the phase plate. The magnetic effect was increased to 2% for the 220 reflection of an iron single-crystal due to the large extinction ratio of the linear polarizer. The method can be applied to magnetic form factor measurements on ferromagnets in general.