In　this　paper,　a　novel　multigrid　method　based　on　Newton　iteration　is　proposed　to　solve　nonlinear　eigenvalue　problems.　Instead　of　handling　the　eigenvalue　lambda　and　eigenfunction　u　separately,　we　treat　the　eigenpair　(lambda,　u)　as　one　element　in　a　product　space　R　x　H01　(S2).　Then　in　the　presented　multigrid　method,　only　one　discrete　linear　boundary　value　problem　needs　to　be　solved　for　each　level　of　the　multigrid　sequence.　Because　we　avoid　solving　large-scale　nonlinear　eigenvalue　problems　directly,　the　overall　efficiency　is　significantly　improved.　The　optimal　error　estimate　and　linear　computational　complexity　can　be　derived　simultaneously.　In　addition,　we　also　provide　an　improved　multigrid　method　coupled　with　a　mixing　scheme　to　further　guarantee　the　convergence　and　stability　of　the　iteration　scheme.　More　importantly,　we　prove　convergence　for　the　residuals　after　each　iteration　step.　For　nonlinear　eigenvalue　problems,　such　theoretical　analysis　is　missing　from　the　existing　literatures　on　the　mixing　iteration　scheme.