LiNbO3 single crystals with uniformity along the growth direction were grown from 0.5 mol% MgO doped 48.6 mol% Li2O melt and Li-rich melts (51.5, 55.0, 58.0 and 60.0 mol% Li2O) by the continuous charging Czochralski method and the double crucible Czochralski method. It was confirmed by measurements of the phase-matching temperature that the Li2O content in seed end and tail end were 50.000 and 50.007+/-0.003 mol% Li2O in the crystal grown from 58 mol% Li2O melt. Difference of Mg concentration between seed end and tail end in the continuous charging Czochralski grown crystals was within +/-0.01 mol% Mg. The melt compositions were kept constant in the crystal growth by the continuous charging Czochralski method. However, a mixing of initial melts between the inner and the outer crucibles occurs before crystal pulling when the crystals are grown by the double crucible Czochralski method from melts with more than 58 mol% Li2O melt.