Based　on　the　smoothing　function　of　penalized　Fischer-Burmeister　NCP-function,　we　propose　a　new　smoothing　inexact　Newton　algorithm　with　non-monotone　line　search　for　solving　the　generalized　nonlinear　complementarity　problem.　We　view　the　smoothing　parameter　as　an　independent　variable.　Under　suitable　conditions,　we　show　that　any　accumulation　point　of　the　generated　sequence　is　a　solution　of　the　generalized　nonlinear　complementarity　problem.　We　also　establish　the　local　superlinear　(quadratic)　convergence　of　the　proposed　algorithm　under　the　BD-regular　assumption.　Preliminary　numerical　experiments　indicate　the　feasibility　and　efficiency　of　the　proposed　algorithm.