The Goos-Hnchen shift at both sides of the waveguide is conducted, which gives rise to a quadric-curve relation between Goos-Hnchen shift and the applied voltage, based on the theoretical analysis of the intrinsic loss in a symmetrical metal-cladding electro-optic waveguide. A symmetrical metal-cladding waveguide is fabricated with a 622 μm-thick Pb(Mg1/3Nb2/3O3)-PbTiO3 (PMN-PT) transparent ceramic which serves as the guiding layer of the waveguide. Measurements of the relation between Goos-Hnchen shift and the applied voltage are carried out and the quadratic electro-optic coefficient of the PMN-PT ceramic is obtained. Experimental results are agreed well with the numerical simulations.