Waveguide　discontinuities　with　anisotropic　dielectric　are　simulated　and　analyzed　by　the　precise　integration　method.　The　discrete　coefficient　matrices　for　the　cross-section　of　the　waveguide,　which　contains　anisotropic　dielectric,　are　deduced　from　the　variational　principle　based　on　single　variable　corresponding　to　the　vector　wave　equation.　Introducing　the　dual-variables,　the　stiff　matrices　are　calculated　by　using　precise　integration　method　in　a　Hamiltonion　system.　Then　the　problem　is　solved　by　assembling　the　finite　elements.　Numerical　results　show　accuracy　and　good　efficiency　of　the　method.　The　influence　of　the　components　of　permittivity　and　permeability　on　the　waveguide　transmission　characteristic　is　also　discussed.