Manufacturing a cold-rolled steel plate, having a steel slab having the chemical composition containing, on the basis of percent by mass, C from 0.03 to 0.08%, Si from 0 to 1.0%, Mn from 0.2 to 0.8%, P at 0.03% or less, S at 0.01% or less, and Al at 0.05% or less so as to satisfy the following: formula (1) and at least one of Nb from 0.03 to 0.4%, V from 0.01 to 0.3%, and Ti from 0.01 to 0.3% so as to satisfy the following formula (2), with a residue being formed of Fe and unavoidable impurities. The steel slab is heated to 1200° C. or more and hot rolled to form a hot-rolled steel plate, which is wound from 550 to 700° C. to form a hot-rolled coil, and the hot-rolled coil is cold rolled or annealed and cold rolled, obtaining cross-sectional hardness from 200 to 350 HV.