In　this　paper,　we　study　an　efficient　multigrid　method　to　solve　the　semilinear　interface　problems.　We　first　give　an　optimal　finite　element　error　estimate　for　the　semilinear　interface　problems　under　a　weak　condition　for　the　nonlinear　term　compared　with　the　existing　conclusions.　Then　next　based　on　the　finite　element　error　estimate,　we　design　a　novel　multigrid　method　for　semilinear　elliptic　problems.　The　proposed　multigrid　method　only　requires　to　solve　a　linear　interface　problem　in　each　level　of　the　multilevel　space　sequence　and　a　small-scale　semilinear　interface　problem　in　a　correction　space.　The　involved　linear　interface　problem　can　be　solved　efficiently　by　the　multigrid　iteration.　The　dimension　of　the　correction　space　is　small　and　fixed,　which　is　independent　from　the　fine　spaces.　Thus　the　computational　time　of　the　correction　step　is　negligible　compared　with　that　of　the　linear　interface　problems　in　the　fine　spaces.　On　the　whole,　the　efficiency　of　the　presented　multigrid　method　is　nearly　the　same　as　that　of　the　multigrid　method　for　linear　interface　problems.　Additionally,　unlike　the　existing　finite　element　error　estimates　and　the　multigrid　methods　for　semilinear　interface　problems,　which　always　require　the　bounded　second　order　derivatives　of　the　nonlinear　terms,　all　the　analysis　in　our　paper　only　requires　a　Lipschitz　continuous　condition.　(C)　2022　IMACS.　Published　by　Elsevier　B.V.　All　rights　reserved.