In　this　paper,　we　study　the　boundary　layer　problem　for　the　two-dimensional　incompressible　MHD　system　with　the　non-characteristic　Dirichlet　boundary　condition　for　the　velocity　and　the　perfect　conducting　wall　boundary　condition　for　the　magnetic　field.　Using　multiscale　analysis　and　the　elaborate　energy　methods,　we　rigorously　prove　that　the　solutions　of　the　viscous　and　diffusive　MHD　system　are　approximated　by　the　inner　solutions　with　the　boundary　layers　in　the　sense　of　L2　norm　when　the　viscosity　and　diffusion　coefficient　tend　to　zero.