Electromagnetic fields in a rectangular conducting waveguide filled with uniaxial anisotropic media are analyzed in this paper using Fourier transform. TE modes and TM modes are found to be related to the ordinary waves and extraordinary waves, respectively. The calculated dispersion curves are depicted and the effects of the material parameters on the cutoff frequencies are shown. The cutoff frequencies change considerably especially for TM modes. The field distributions are plotted to compare with the isotropic rectangular waveguide. The electric type dyadic Green's function due to electric source is derived in the form of vector wave functions expansion by applying Ohm-Rayleigh method. The final result shows that the parameters of the medium have close and intricate relationships with the properties of the Green's function, hence, influencing the propagation of the guided wave. The dyadic Green's function is reducible to that in the isotropic medium. From Maxwell equations, the magnetic dyadic Green's function due to electric source is also given. As the application of the dyadic Green's functions, numerical results of the fields inside the waveguide excited by an infinitesimal dipole are present.