The　regularity　for　the　2D　incompressible　MHD　equations　with　partial　dissipation　and　magnetic　diffusion　was　studied.　A　regularity　criteria　was　given　for　the　2D　incompressible　MHD　equations　with　partial　dissipation　and　magnetic　diffusion　(The　velocity　field　and　the　magnetic　field　had　the　partial　derivative　of　two-order　type　only　in　the　same　one　direction).　It　is　proved　that　the　uniqueness　local　classical　solution　of　the　2D　incompressible　MHD　equations　with　partial　dissipation　and　magnetic　diffusion　will　be　global　if　the　partial　derivative　of　magnetic　in　one　direction　satisfies　one　regularity　criteria.