A thermal refiningless, hot-rolled steel exhibits impact strength in excess of 10kgf.multidot.m/cm.sup.2 and contains, expressed in terms of weight percent, 0.30-0.50% carbon, 0.15-0.60% silicon, 0.80-1.60% manganese, up to 0.02% phosphorus, up to 0.015% sulfur, 0.07-0.20% vanadium, 0.015-0.06% aluminum, 0.005-0.015% nitrogen, up to 0.0015% oxygen, the balance iron and unavoidable impurities. The steel of the above-identified property and composition is produced by casting a steel product of predetermined cross-sectional shape; heating the steel product up to a temperature of 1,100.degree.-1,250.degree. C.; hot-rolling the heated steel product at a final rolling temperature of 850.degree.1,000.degree. C.; normalizing the hot-rolled steel product at a temperature of 880.degree.-950.degree. C.; and cooling the normalized steel product down to 300.degree. C. at a cooling speed of 5.degree.-100.degree. C./min.