A high-strength cold-rolled steel sheet having high chemical convertibility and a tensile strength of 590 MPa or more and a method for producing such a steel sheet are provided. The steel sheet contains, in terms of percent by mass, C: 0.05 to 0.3%, Si: 0.6 to 3.0%, Mn: 1.0 to 3.0%, P: 0.1% or less, S: 0.05% or less, Al: 0.01 to 1%, N: 0.01% or less, and the balance being Fe and unavoidable impurities. The coverage ratio of reduced iron on a steel sheet surface is 40% or more. In order to produce such a steel sheet, an oxidation treatment is performed after cold rolling. In the oxidation treatment, first heating is conducted on a steel sheet in an atmosphere with an oxygen concentration of 1000 ppm or more until the steel sheet temperature reaches 630 DEG C or higher and then second heating is conducted on the steel sheet in an atmosphere with an oxygen concentration of less than 1000 ppm until the steel sheet temperature reaches 700 DEG C or higher. Subsequently, annealing is conducted in a furnace in a 1 to 10 vol% H 2 + balance N 2 gas atmosphere with a dew point of -25 DEG C or less.