PROBLEM TO BE SOLVED: To provide a useful method for producing a cold rolled steel sheet capable of suppressing a pickup flaw on the basis of the formation of reduced iron and even a pickup flaw on the basis of the oxidization of a steel sheet surface, and excellent in surface quality.SOLUTION: When a steel sheet is annealed in a continuous annealing furnace having a non-oxidative atmosphere following cold rolling, the annealing is performed while the vicinity of a feed roll having a temperature of 600°C or more is in the atmosphere of a gas composition having an oxygen concentration of less than 100 ppm (hereinafter, the same in a volume reference and a gas concentration) and a hydrogen concentration of 200 ppm or more and satisfying a relation of following formula (1), a hydrogen concentration (ppm)×0.04
