High-quality $Er^{3+}$ doped Mg : $LiNbO_3$single crystal fibers were grown by a micro-pulling down ($mu$-PD) method. Single crystal fibers were pulled down through the nozzle, at a pulling down rate of 0.5 mm/min and using a Pt crucible with a nozzle 1 mm in diameter in air atmosphere. Defects such as bubbles, cracks and inclusions were not detected in any of the grown crystals. The optical transmission of Er : Mg : $LiNbO_3$crystal was measured and the energy levels of $Er_2O_3$ ion could be calculated. The photoluminescence spectrum of crystal fibers showed an energy band emission with the strongest line corresponding to the $^4I_{3/2}{ o}^4I_{15/2}$transition. The concentration dependence of the entire wavelength region emission intensity upon excitation intensity measured emission intensity for the 3 mol% MgO doped fibers was larger than that for the 1, 5 mol% MgO doped fibers.