This　paper　presents　a　modified　least-squares　finite　element　method　for　solving　the　Boltzmann　transport　equation　with　spherical　harmonics　angular　approximation　(LSPN).　Traditional　LSPN　methods　usually　adopt　weakly　imposed　boundary　conditions　which　contain　an　uncertain　parameter　and　it　may　lead　to　inaccurate　results　without　proper　scaling　for　problems　with　sharp　cross　section　interfaces.　In　order　to　eliminate　the　discretization　error　at　material　interface　and　use　continuous　interface　condition,　we　multiply　a　scaling　parameter　to　least-squares　term　and　add　the　weak　form　of　the　first-order　transport　equation.　With　this　method,　the　natural　boundary　condition　can　be　applied　directly　and　the　scaling　parameter　is　identified　as　the　minimal　value　of　characteristic　length　of　element　and　the　reciprocal　of　removal　cross　section.　The　method　is　verified　by　various　benchmark　problems　and　the　numerical　results　show　it　has　high　accuracy,　stability　and　void　applicability.　©　2019　Elsevier　Ltd