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.