Micro-defects in the undoped and MgO-doped $LiNbO_3$ single crystals, which were grown from a congruent melting composition (48.6 mol% $Li_2$O) by the CZ (Czochralski) method, were analyzed using microscopic techniques such as optical microscopy (OM), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Effects of the dopant and g value (the fraction solidfied) on the domain structure and micro-defect were investigated to build a corelationship with a growth condition of crystal. It was observed that the micro-defect concentrated near the domain wall is caused by high stress. Especially, the micro-defect was observed to be biased toward a certain side of the domain wall.