The present invention provides a steel sheet having a chemical composition comprising 0.15% or less C, 2.0% or less Si, 3.0% or less Mn, P, S, Al and N in adjusted amounts, from 0.5 to 3.0% Cu, or one or more of Cr, Mo and W in a total amount of 2.0% or less, and having a composite structure comprising ferrite and martensite having an area ratio of 2% or more. The steel sheet is in the form of a high-strength hot-rolled steel sheet, a high-strength cold-rolled steel sheet, or a hot-dip galvanized steel sheet. There is thus available a steel sheet excellent in press-formability and in strain age hardening property as represented by a .DELTA.TS of 80 MPa or more.