This　article　introduces　a　new　kind　of　multigrid　approach　for　semilinear　elliptic　problems,　which　is　based　on　the　symmetric　interior　penalty　discontinuous　Galerkin　(SIPDG)　method.　We　first　give　an　optimal　error　estimate　of　the　SIPDG　method　for　the　problem.　Then,　we　design　a　type　of　multigrid　method,　which　is　called　the　multilevel　correction　method,　and　derive　a　priori　error　estimates.　The　primary　idea　of　this　method　is　to　take　the　solution　of　the　semilinear　problem　and　utilize　it　to　establish　a　sequence　of　solutions　for　associated　linear　boundary　value　problem　on　discontinuous　finite　element　spaces　and　a　newly　defined　low　dimensional　augmented　subspace.　Lastly,　numerical　experiments　are　offered　to　confirm　the　suggested　method＇s　precision　and　effectiveness.