The Faraday rotation of two-dimensional magnetophotonic crystals （including those with fourfold-symmetry and non-fourfold-symmetry） with structural defects and the ellipticity of outgoing optical waves are analyzed by using finite-difference frequency-domain （FDFD） method. The numerical simulation results show that the localization of the light wave in the vicinity of central defect occurs in these types of the structure. With increasing Faraday rotation of fourfold-symmetry structures, the change of the ellipticity of outgoing optical waves from these structures is unobvious. In contrast, the increases of the ellipticity of outgoing optical waves are obvious with the raise of Faraday rotation in non-fourfold-symmetry structures. It is concluded that introducing defects to the fourfold-symmetry structure constrains the change of the state of polarization of optical waves. This kind of two-dimensional magnetophotonic crystal with structural defects may be used to manufacture magnetophotonic crystal fiber.