The present invention provides a high-strength cold-rolled steel sheet and a high-strength surface treated steel sheet 780 MPa or more in tensile strength, said steel sheets having excellent local formability and suppressed weld hardness increase and being characterized by: said steel sheets containing, in weight, C: 0.05 to 0.09%, Si: 0.4 to 1.3%, Mn: 2.5 to 3.2%, P: 0.001 to 0.05%, N: 0.0005 to 0.006%, Al: 0.005 to 0.1%, Ti: 0.001 to 0.045%, and S in the range stipulated by the following expression (A), with the balance consisting of Fe and unavoidable impurities; the microstructures of said steel sheets being composed of bainite of 7% or more in terms of area percentage and the balance consisting of one or more of ferrite, martensite, tempered martensite and retained austenite; and said components in said steel sheets satisfying the following expressions (C) and (D) when Mneq. is defined by the following expression (B); S≦0.08×(Ti(%)−3.43×N(%)+0.004 . . . (A), where, when a value of the member Ti(%)−3.43×N(%) of said expression (A) is negative, the value is regarded as zero. MIneq.=Mn(%)−0.29 ×Si(%)+6.24×C(%) . . . (B), 950≦(Mneq./(C(%)−(Si(%)/75)))×bainite area percentage (%) . . . (C), C(%)+(Si(%)/20)+(Mn(%)/18)50.30 . . . (D).