$LiNbO_{3}$ single crystals were grown using a self-designed radio-frequency heating Czochralski crystal grower. Congruently melting composition was used and the optimum growth conditions were established. The compensated power control method was very effective to control the outer diameter of the crystal ingots within ${pm}5;%$. Scanning electron microscopy was performed to characterize the effect of the $Mg^{2+}$ ions on the formation of the ferroelectric domain in $LiNbO_{3}$.