A process for producing amethyst crystals involving growing of colorless quartz crystals by a hydrothermal method of a temperature drop in a high-pressure autoclave on crystalline quartz seed plates oriented parallel to the crystallographic planes of the major {1011} and minor {1101} rhombohedrons using crystalline quartz as a charge. Said growing is effected from aqueous solutions of potassium carbonate or potassium hydroxide having a concentration ranging from 4 to 7 wt.% and containing iron introduced into the autoclave in the form of metallic iron or in the form of its oxydic or hydroxydic compounds in an amount ranging from 5 to 30 g/l of the solution. The growing process is effected at a crystallization temperature within the range of from 300.degree. to 500.degree. C. under a pressure ranging from 200 to 1,700 kg/cm.sup.2 and a crystal growth rate of from 0.05 to 0.5 mm/day. It is advisable to introduce into the autoclave, prior to the crystal growing, lithium nitrite or lithium nitrate or manganese nitrate in an amount ranging from 1 to 10 g/l of the solution. The thus-grown colorless quartz crystals are exposed to an ionizing irridation. The process for growing crystals according to the present invention is well-reproducible, since it is performed at specfied physico-chemical parameters. The process of the present invention enables the production of amethyst crystals with a high color purity and a high transparency (i.e., with no cracks).