In　this　paper,　we　consider　the　wave　propagation　with　Debye　polarization　in　nonlinear　dielectric　materials.　The　Rothe＇s　method　is　employed　to　derive　the　well-posedness　of　the　electric　fields　and　the　polarized　fields　by　monotonicity　theorem　as　well　as　the　boundedness　of　the　two　fields　are　established.　Then,　the　decoupled　full-discrete　scheme　is　established　with　the　first　order　approximation　in　time　and　Raviart-Thomas-Nedelec　element　k　＞=　2　in　spatial.　Based　on　the　truncated　error,　we　present　the　convergent　analysis　with　the　order　O　(Delta　t　+　h(s))　under　an　a-prior　L-infinity　assumption　of　numerical　solutions.　For　k　=　1,　we　employ　the　superconvergence　technique　to　ensure　the　a-prior　L-infinity　assumption.　In　the　end,　we　give　some　numerical　examples　to　demonstrate　our　theories.　(C)　2019　IMACS.　Published　by　Elsevier　B.V.　All　rights　reserved.