In　this　paper　we　study　the　model　that　the　usual　Maxwell＇s　equations　are　supplemented　with　a　constitution　relation　in　which　the　electric　displacement　equals　a　constant　time　the　electric　field　plus　an　internal　polarization　variable　and　the　magnetic　displacement　equals　a　constant　time　the　magnetic　field　plus　the　microscopic　magnetization.　Using　the　Galerkin　method　and　viscosity　vanishing　approach,　we　obtain　the　existence　of　the　global　weak　solution　for　the　Landau-Lifshitz-Maxwell　equations.　The　main　difficulties　in　this　study　are　due　to　the　loss　of　compactness　in　the　system.