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.