A　novel　fully　discrete　two-grid　finite　element　method　for　certain　semi-linear　parabolic　equations　is　presented　in　this　paper.　The　new　scheme　is　based　on　two　different　finite　element　subspaces　defined　respectively　on　one　coarse　grid　with　grid　size　H　and　one　fine　grid　with　grid　size　h　＜＜　H.　Nonlinearity　is　treated　in　the　coarse　grid　subspace　by　solving　the　standard　Galerkin　equation,　while　in　the　fine　grid　subspace,　only　a　linear　equation　has　to　be　solved.　Differing　from　the　usual　two-grid　method,　the　splitting　of　the　coarse　grid　subspace　and　its　related　fine　grid　incremental　subspace　is　based　on　a　new　projection,　in　which　sense　the　incremental　subspace　is　closely　identified　with　the　tangent　space　of　certain　operator　on　each　time　step.　With　linear　finite　element　discretization,　the　stability　and　error　estimate　results　for　such　new　scheme　are　derived.　The　results　show　that　the　difference　between　this　new　approximation　and　the　fine　grid　standard　Galerkin　approximation　in　H-1(Q)　norm　is　of　the　order　H4-2/d　in　H-2/d　where　d　=　1,2,3　is　the　space　dimension.　(c)　2005　Elsevier　Inc.　All　rights　reserved.