A zinc or zinc alloy coated steel excellent in various properties including corrosion resistance and adhesion properties and, in particular, good conductivity is provided. A method for manufacturing a zinc or zinc alloy coated steel sheet includes: preparing a surface-treatment liquid for a the steel sheet, containing following components, by blending the including: (A) a specific resin emulsion; (B) a tetraalkoxysilane; (C) at least one type of silane coupling agent; (D) a chelating agent; (E) a vanadate compound; (F) a titanium compound; and water; and applying by coating the surface-treatment liquid to a surface of the steel sheet, heating and drying the surface of the steel sheet such that a coating amount per one surface is 200 to 1,000 mg/m2 to form a surface treatment coating film on the surface.