A perpendicular STT-MRAM comprises apparatus and a method of manufacturing a plurality of magnetoresistive memory element having local magnetic shielding. As an external perpendicular magnetic field exists, the permeable dielectric layers, the permeable bit line and the permeable bottom electrode are surrounding and have capability to absorb and channel most magnetic flux surrounding the MTJ element instead of penetrate through the MTJ element. Thus, magnetization of a recording layer can be less affected by the stray field during either writing or reading, standby operation.