The　purpose　of　this　paper　is　to　study　the　boundary　layer　problem　and　zero　viscosity-diffusion　limit　of　the　initial　boundary　value　problem　for　the　incompressible　viscous　and　diffusive　magnetohydrodynamic　(MHD)　system　with　(no-slip　characteristic)　Dirichlet　boundary　conditions　and　to　prove　that　the　corresponding　Prandtl＇s　type　boundary　layer　are　stable　with　respect　to　small　viscosity-diffusion　coefficients.　The　main　difficulty　here　comes　from　Dirichlet　boundary　conditions　for　the　velocity　and　magnetic　field.　Firstly,　we　identify　a　non-trivial　class　of　initial　data　for　which　we　can　establish　the　uniform　stability　of　the　Prandtl＇s　type　boundary　layers　and　prove　rigorously　the　solution　of　incompressible　viscous-diffusion　MHD　system　converges　strongly　to　the　sum　of　the　solution　to　the　ideal　MHD　system　and　the　approximating　solution　to　Prandtl＇s　type　boundary　layer　equation　by　using　the　elaborate　energy　methods　and　the　special　structure　of　the　solution　to　ideal　MHD　system　with　the　initial　data　we　identify　here,　which　yields　that　there　exists　the　cancellation　between　the　boundary　layer　of　the　velocity　and　that　of　the　magnetic　field.　Secondly,　for　general　initial　data,　we　obtain　zero　viscosity-diffusion　limit　of　the　incompressible　viscous　and　diffusive　MHD　system　with　the　different　horizontal　and　vertical　viscosities　and　magnetic　diffusions,　when　they　go　to　zero　with　the　different　speeds,　and,　we　prove　rigorously　the　convergence　of　the　incompressible　viscous　and　diffusion　MHD　system　to　the　ideal　MHD　system　or　the　anisotropic　MUD　system　by　constructing　the　exact　boundary　layers　and　using　the　elaborate　energy　methods.　We　also　mention　that　these　results　obtained　here　should　be　the　first　rigorous　ones　on　the　stability　of　Prandtl＇s　type　boundary　layer　for　the　incompressible　viscous　and　diffusion　MED　system　with　no-slip　characteristic　boundary,　condition.　(C)　2017　Elsevier　Inc.　All　rights　reserved.