A high strength cold-rolled steel sheet has excellent surface appearance and a composition consisting essentially of, in mass %, C: 0.0005-0.025%, Si: at most 0.2%, Mn: 0.3-2.5%, P: at most 0.15%, S: at most 0.02%, N: at most 0.006%, sol. Al: less than 0.005%, Ti: 0.005-0.05%, and Nb: 0.020-0.200% with the mass ratio (Nb/Ti) of the contents of Nb and Ti being at least 2, either boron at most 0.0020% or one or more of Cr, Mo, V, W, Cu, and Ni, each at most 1%, and a remainder of Fe and impurities. The sheet has excellent press formability and tensile strength by having an r value in a direction at 45° with respect to the rolling direction (r45) of at least 1.80 and/or a mean r value (rm) of at least 1.60, and a tensile strength of at least 340 MPa.