In this paper we studied the general forms and properties of tensor Green functions in waveguides with the methods of eigenfunctions expansion. For acquiring relations between the eigenfunctions of waveguides and tensor Green function, we first take the Fourier transform of Green function. In isotropic media the simplest image function can be expressed in dyadic form, and in anisotropic media in the form of ABA+e-ikz0,where A is the coordinate matrix. With this method, we studied the dyadic Green functions of waveguides in isotropic media in detail.