To　handle　the　control　rod　cusping　effect　in　pressurized　water　reactor　(PWR)　fuel　management　calculation,　the　variational　nodal　method　(VNM)　in　the　fuel　management　calculation　code　system　NECP-Bamboo　has　been　extended　to　tread　the　heterogeneous　cross　section　distribution　by　expanding　the　volumetric　cross　sections　into　piece-wise　polynomials　in　the　early　work.　However,　the　partially　inserted　control　rods　also　introduces　heterogeneous　discontinuity　factor　(DF)　on　nodal　interface.　Thus,　in　this　paper,　an　ultimate　solution　is　proposed　to　fully　handle　this　problem.　Firstly,　the　surface　integral　in　the　VNM　is　modified　to　contain　the　discontinuity　of　neutron　flux,　incorporating　a　continuous　discontinuity　factor　in　that　term.　Secondly,　the　surface　DF　is　expanded　into　the　sum　of　pieces-wise　orthogonal　polynomials　to　construct　the　nodal　response　matrixes.　Comparing　with　current　representative　re-homogenization　methods,　the　application　numerical　results　of　the　BEAVRS　benchmark　problem　demonstrate　the　effectiveness　of　the　heterogeneous　VNM　with　heterogeneous　DF.　It　can　eliminate　the　cusping　effect　by　providing　more　accurate　differential　control　rode　worth　curves　and　pin　power　distributions.　©　2020,　Editorial　Board　of　Journal　of　Nuclear　Power　Engineering.　All　right　reserved.