A cold-rolled steel sheet that is suitable for battery cases and has low anisotropy is composed of, by mass %, C: ≦0.0030%, Si: ≦0.02%, Mn: 0.15 to 0.19%, P: ≦0.020%, S: ≦0.015%, N: ≦0.0040%, Al: 0.020 to 0.070%, Nb: 1.00≦Nb/C (atomic equivalent ratio)≦5.0, B: 1 ppm≦B-(11/14)N≦15 ppm (in the expression, B and N denote the contents of the respective elements), and the balance: being Fe and inevitable impurities, and has a planar anisotropy Δr of the r-value in the range of −0.10≦Δr≦0.10. In a process for producing the steel sheet, the cold rolling is performed at a rolling ratio of 70 to 87%, and then annealing is performed on a continuous annealing line at an annealing temperature of from the recrystallization temperature to 830° C.