A method for producing a hot-rolled steel sheet, a method for producing a cold-rolled full-hard steel sheet, and a method for producing a heat-treated sheet are provided herein. The methods comprising hot rolling a steel material of a composition comprising, in mass %, C: 0.05 to 0.12%, Si: 0.80% or less, Mn: 1.30 to 2.10%, P: 0.001 to 0.050%, S: 0.005% or less, Al: 0.01 to 0.10%, N: 0.010% or less, one or more selected from Cr in an amount of 0.05 to 0.50%, and Mo in an amount of 0.05 to 0.50%, one or more selected from Ti in an amount of 0.01 to 0.10%, Nb in an amount of 0.01 to 0.10%, and V in an amount of 0.01 to 0.10%, and the balance Fe and unavoidable impurities.