A method of producing a cold rolled steel strip comprising: subjecting a steel strip containing 0.5 mass% to 3.0 mass% of Si that has been cold rolled and subsequently continuously annealed to pickling by continuously feeding the steel strip into a mixed acid solution containing a first acid that is nitric acid and a second acid that is at least one selected from the group consisting of hydrochloric acid, sulfuric acid, phosphoric acid, pyrophosphoric acid, formic acid, acetic acid, citric acid, hydrofluoric acid, and oxalic acid to immerse the steel strip; and subsequently subjecting the steel strip to repickling by continuously feeding the steel strip into an acid solution containing a third acid that is at least one selected from the group consisting of hydrochloric acid, sulfuric acid, phosphoric acid, pyrophosphoric acid, formic acid, acetic acid, citric acid, hydrofluoric acid, and oxalic acid to immerse the steel strip, wherein concentration of the first acid in the mixed acid solution is set within a range of higher than 110 g/L and not higher than 188 g/L, and concentration of the second acid in the mixed acid solution is set within a range of higher than 4.5 g/L and not higher than 12.5 g/L, concentration of the third acid in the acid solution is set within a range of higher than 4.5 g/L and not higher than 12.5 g/L, Fe concentration in the mixed acid solution is measured over time, and the concentration of the first acid in the mixed acid solution is lowered and the concentration of the second acid in the mixed acid solution is raised so as to maintain the temperature of the mixed acid solution constantly within a range of 45 °C to 55 °C as the Fe concentration in the mixed acid solution rises in a manner such that: (i) a number of levels of the Fe concentration is predetermined, set concentrations for the first acid and the second acid are predetermined for each level, and when the measured Fe concentration transitions to a next level, the concentrations of the first acid and the second acid are adjusted, or (ii) a relationship formula between the Fe concentration and set concentrations for the first acid and the second acid is predetermined, and the concentrations of the first acid and the second acid are adjusted from moment to moment in accordance with the relationship formula with a gradual rise in the measured Fe concentration in the mixed acid. subjecting a steel strip containing 0.5 mass% to 3.0 mass% of Si that has been cold rolled and subsequently continuously annealed to pickling by continuously feeding the steel strip into a mixed acid solution containing a first acid that is nitric acid and a second acid that is at least one selected from the group consisting of hydrochloric acid, sulfuric acid, phosphoric acid, pyrophosphoric acid, formic acid, acetic acid, citric acid, hydrofluoric acid, and oxalic acid to immerse the steel strip; and subsequently subjecting the steel strip to repickling by continuously feeding the steel strip into an acid solution containing a third acid that is at least one selected from the group consisting of hydrochloric acid, sulfuric acid, phosphoric acid, pyrophosphoric acid, formic acid, acetic acid, citric acid, hydrofluoric acid, and oxalic acid to immerse the steel strip, wherein concentration of the first acid in the mixed acid solution is set within a range of higher than 110 g/L and not higher than 188 g/L, and concentration of the second acid in the mixed acid solution is set within a range of higher than 4.5 g/L and not higher than 12.5 g/L, concentration of the third acid in the acid solution is set within a range of higher than 4.5 g/L and not higher than 12.5 g/L, Fe concentration in the mixed acid solution is measured over time, and the concentration of the first acid in the mixed acid solution is lowered and the concentration of the second acid in the mixed acid solution is raised so as to maintain the temperature of the mixed acid solution constantly within a range of 45 °C to 55 °C as the Fe concentration in the mixed acid solution rises in a manner such that: (i) a number of levels of the Fe concentration is predetermined, set concentrations for the first acid and the second acid are predetermined for each level, and when the measured Fe concentration transitions to a next level, the concentrations of the first acid and the second acid are adjusted, or (ii) a relationship formula between the Fe concentration and set concentrations for the first acid and the second acid is predetermined, and the concentrations of the first acid and the second acid are adjusted from moment to moment in accordance with the relationship formula with a gradual rise in the measured Fe concentration in the mixed acid. (i) a number of levels of the Fe concentration is predetermined, set concentrations for the first acid and the second acid are predetermined for each level, and when the measured Fe concentration transitions to a next level, the concentrations of the first acid and the second acid are adjusted, or (ii) a relationship formula between the Fe concentration and set concentrations for the first acid and the second acid is predetermined, and the concentrations of the first acid and the second acid are adjusted from moment to moment in accordance with the relationship formula with a gradual rise in the measured Fe concentration in the mixed acid.