A high strength cold rolled strip having excellent deep drawability and resistance to deterioration by natural aging and to planar cracking and useful for motor vehicles, is produced by hot rolling a steel slab comprising0.008-0.020% by weight of C,0.01-0.45% by weight of Mn,0.05-0.10% by weight of P,0.005-0.050% by weight of acid-soluble Al,and the balance consisting of Fe and unavoidable impurities in which N is limited to a content of 40 ppm or less, at a temperature of 1200.degree. C. or less but not lower than the Ar.sub.3 point of the steel slab; by cold rolling the resultant steel strip at a rolling reduction of 65% or more; by continuously annealing the cold rolled steel strip at a temperature of from 700.degree. to 900.degree. C. for 20 seconds to 3 minutes; by cooling the steel strip at a cooling rate of 5.degree. C./sec or more; by overaging the annealed steel strip at a temperature of from 320.degree. to 450.degree. C. for 1 to 10 minutes; by cooling said overaged steel strip to the ambient temperature, and, finally; by temper-rolling the cooled steel strip at the ambient temperature.