A transfer-matrix method is used to study the distribution and polarization of circular waves in a waveguide with circular gratings. The method enables us to design gratings for a TE or TM wave. If the waveguide is a weak one, the in-plane components of the electrical field of a TM wave are small and the wave can be regarded as linearly polarized. If the waveguide does not have TE-TM wave birefringence, we find that a mixture of a TM1 wave with a small portion of TE1 wave is a linearly polarized LP0 wave in the waveguide plane. However, unlike the LP0 wave in a fiber, the in-plane component of the electrical field is not circularly symmetric.