In　this　paper,　a　new　type　of　local　and　parallel　algorithm　is　proposed　to　solve　nonlinear　eigenvalue　problem　based　on　multigrid　discretization.　Instead　of　solving　the　nonlinear　eigenvalue　problem　directly　in　each　level　mesh,　our　method　converts　the　nonlinear　eigenvalue　problem　in　the　finest　mesh　to　a　linear　boundary　value　problem　on　each　level　mesh　and　some　nonlinear　eigenvalue　problems　on　the　coarsest　mesh.　Further,　the　involved　linear　boundary　value　problems　are　solved　using　the　local　and　parallel　strategy.　As　no　nonlinear　eigenvalue　problem　is　being　solved　directly　on　the　fine　spaces,　which　is　time-consuming,　this　new　type　of　local　and　parallel　multigrid　method　evidently　improves　the　efficiency　of　nonlinear　eigenvalue　problem　solving.　We　provide　a　rigorous　theoretical　analysis　for　our　algorithm　and　present　details　on　numerical　simulations　to　support　our　theory.