A　full　multigrid　finite　element　method　is　proposed　for　semilinear　elliptic　equations.　The　main　idea　is　to　transform　the　solution　of　the　semilinear　problem　into　a　series　of　solutions　of　the　corresponding　linear　boundary　value　problems　on　the　sequence　of　finite　element　spaces　and　semilinear　problems　on　a　very　low　dimensional　space.　The　linearized　boundary　value　problems　are　solved　by　some　multigrid　iterations.　Besides　the　multigrid　iteration,　all　other　efficient　numerical　methods　can　also　serve　as　the　linear　solver　for　solving　boundary　value　problems.　The　optimality　of　the　computational　work　is　also　proved.　Compared　with　the　existing　multigrid　methods　which　need　the　bounded　second　order　derivatives　of　the　nonlinear　term,　the　proposed　method　only　needs　the　Lipschitz　continuation　in　some　sense　of　the　nonlinear　term.