A series of Mg2+/Er3+-codoped congruent LiNbO3 crystals were grown by Czochralski method from the growth melts containing 0.5 mol% Er2O3 while varied MgO content from 0.0 to 7.0 mol%. The unclamped electro-optic coefficients (13) and (33) of these crystals were measured by Mach-Zehnder interferometry. Two different voltage-applying schemes were adopted: one is the DC voltage applied to the crystal via Al films coated onto crystal surfaces and another is via a pair of external Cu slab electrodes. The coefficients measured by the two schemes show similar strong dependence on Mg2+ concentration. The dependence is non-monotonous, dramatic, and unusual, and reveals the features of two Mg2+ concentration thresholds of optical damage: one in the Mg2+ concentration range of 1.2-2.0 mol% (in crystal) and another in 4.5-5.0 mol%. Around the threshold the electro-optic coefficient decreases abruptly at first and then recovers quickly, and the coefficient drops by >20% (12%) at the first (second) threshold, which exceeds the error 3% considerably. The dramatic behavior is qualitatively explained on the basis of the EO coefficient model of LiNbO3 and the defect structure model for Mg2+-doped LiNbO3.