Disclosed are: a cold-rolled steel sheet which undergoes less load during cold rolling and has excellent press moldability and high strength; and a process for producing the cold-rolled steel sheet. A hot-rolled steel sheet comprising 0.10 to 0.30 mass% of C, 0.2 mass% or more of Mn, 0.01 mass% or more of Ni (wherein the sum total of Mn and Ni is 0.5 to 2.5 mass%), and 1.2 to 9.0 mass% of Cr, with the remainder being iron and unavoidable impurities, and having a tensile strength of 1000 MPa or less is washed with an acid, and is subjected to cold rolling at a total rolling ratio of 60% or more, thereby producing a cold-rolled steel sheet. The cold-rolled steel sheet is subjected to the final continuous annealing treatment at a homogenizing temperature of 750 DEG C or higher and a cooling rate of 3 to 100 DEG C/s. In this manner, a cold-rolled steel sheet having a tensile strength of 1280 MPa or more, a breaking elongation of 3% or more, and a thickness of 0.05 to 0.60 mm.