Laser‐quality yttrium‐aluminum garnet single crystals doped with neodymium (YAG:Nd) of a concentration up to 1 at. % is grown by the method of horizontal directional crystallization from a molybdenum crucible in the protective reducing atmosphere based on argon, СО, and hydrogen. It is found that the content of carbon impurity in the grown crystals does not exceed 5·10−3 wt %, the content of molybdenum being on the level of 1.5·10−3 wt %. The optical quality of the crystals depends on the composition of the growth atmosphere and annealing. It is shown that, besides the bands of neodymium ion absorption, the crystals are characterized by the intense absorption in the UV edge of the spectrum at 370 nm wavelength, and by the wide absorption band with a maximum at 580 nm caused by formation of F and F+‐centers. The absorption at 370 and 580 nm can be eliminated by annealing. The structure perfection of the crystals is characterized by the rocking curve half‐width (β) which value varies within the limits of 10–14 arc. sec for (001) plane. Laser testing demonstrates the parameters comparable with those of YAG:Nd crystals grown by the Czochralski method from iridium crucible.