Based on the eigenfunction expansion of electromagnetic waves in the reciprocal uniaxial bianisotropic medium, an extended mode-matching method is developed to study the electromagnetic scattering of a PEC circular cylinder with an inhomogeneous coating thickness of reciprocal uniaxial bianisotropic medium. Excellent convergence property of the bistatic echo width is numerically verified, which establishes the reliability and applicability of the present extended mode-matching method for two-dimensional problem of reciprocal uniaxial bianisotropic medium.