Congruent $LiNbO_3$ single crystals and $LiNbO_3$ : Mg single crystals, having high resistance to optical damage, doped with MgO to the levels of 2.0, 5.0 and 7.0 mol% were grown successfully by CZ method and optical damage of each crystal was measured by compen. sation method. With doping level reaching about 5 mol%, there was an abrupt change in the features of optical absorption edge and $OH^-$ absorption band. From these data, we confirmed indirectly the threshold in MgO doping level. When the MgO doping amount reaches about 5 mol% in the melt, $Mg^{2+}$ occupies Nb site and becomes $Mg_{Nb}^{2+}$, resulting in the sharp increase of optical damage resistance. The optical damage resistance of $LiNbO_3$ : Mg was improved more than three times when MgO amount in the melt reaches 5 mol%.