A semiconductor memory device includes memory cells, first wirings, a first current driver circuit, and a second current driver circuit. The memory cell includes a magneto-resistive element having a first ferromagnetic film, an insulating film formed on the first ferromagnetic film, and a second ferromagnetic film formed on the insulating film. The first wiring is provided in close proximity to and insulated from the magneto-resistive element. The first current driver circuit supplies a first current to the first wiring in a write operation to produce a magnetic field around the magneto-resistive elements. The second current driver circuit supplies a second current between the first and second ferromagnetic films via the insulating film in a write and a read operation.