The invention provides a useful process in which a steel material for obtaining a steel wire material reduced in the content of hard non-rollable inclusions and having enhanced drawability and enhanced fatigue characteristics is produced by adequately controlling conditions in secondary refining and production conditions in a converter. Molten iron, cold pig iron, and scrap steel are used as major raw materials to be charged into a converter, the proportions of the molten iron, cold pig iron, and scrap steel being 96-100 mass%, 4 mass% or lower, and 2 mass% or lower, respectively, based on the whole major raw materials. Blowing in the converter is conducted while the average phosphorus concentration in the whole major raw materials is regulated to 0.02 mass% or lower. After completion of the blowing in the converter, secondary refining is conducted while regulating the flow rate of a molten-iron stirring gas to 0.0005-0.004 Nm3/min per ton of the molten iron. Subsequently, continuous casting is conducted while the flow rate of argon supplied for purging into a tundish is regulated to 0.04-0.10 Nm3/min per ton of the molten iron in the tundish.