Using LiF and YF3 as starting materials, we prepare feed material from fluorides according to the molar ratio of LiF:YF3 = 51.5:48.5. The anhydrous LiYF4 polycrystalline material is synthesized via the fluoridation process with a dried HF flow at elevated temperature. By charging the feed material and adding a small amount of active carbon powder in a sealed platinum crucible, the crystal can be grown via the vertical Bridgman method in a nonvacuum atmosphere. This is possible because the oxidization and volatilization of the melt is avoided. Using optimum conditions, that is, a growth rate of 0.5–0.6 mm/h and a temperature gradient of 25–30 oC/cm across the solid-liquid interface under a furnace temperature of 920–930 oC, the colorless crystal LiYF4 with the size of \phi 25 \times 50 (mm) is successfully grown. The optical transmittance of the crystal is as high as 85% above the absorption edge at 190 nm. The induced absorption bands are observed below 700 nm in the transmission spectrum after the crystal is subjected to a high dose of \gamma-ray irradiation.