The　spectral　element　combined　with　precise　integration　method　was　used　to　simulate　and　analyze　the　waveguide　discontinuities　with　anisotropic　dielectric.　With　the　variational　principle　based　on　single　variable　corresponding　to　the　vector　wave　equation,　spectral　elements,　a　special　type　of　higher　order　finite　element　with　sampling　points　defined　as　the　Gauss-Lobatto-Legendre　points,　were　employed　to　discretize　the　cross　section　of　the　waveguide　structure,　which　contains　anisotropic　dielectric.　Then　the　semidiscretized　problem　was　cast　into　Hamilton　system　and　sloved　by　the　precision　integration　method.　With　adopting　the　spectral　elements,　high　precision　of　calculation　results　can　be　obtained　under　the　low　number　of　unit　grids;　With　the　precise　integration　method,　the　longitudinal　length　of　structure　can　be　set　arbitrarily.　It　can　overcome　the　weakness　of　increasing　computation　amounts　as　lengthening　the　distance　from　artificial　boundary　to　dielectric　block.　Results　show　that　semi-analytical　spectral　element　method　can　be　used　to　effectively　solve　waveguide　discontinuities　problems,　which　contains　anisotropic　dielectric.　The　proposed　methords　is　demanstrated　to　solve　waveguide　discontinuities　problems　with　high　computational　accuracy　and　efficiency.　©,　2015,　Chinese　Optical　Society.　All　right　reserved.