A method for manufacturing a zinc or zinc alloy coated steel sheet, comprising: preparing a surface-treatment liquid for a zinc or zinc alloy coated steel sheet, containing following components, by blending the components in amounts, in solid mass contents calculated from respective masses of the components, which satisfy conditions to below at pH in the range of 3 to 6, the components including: a resin emulsion formed of (A-1) a cationic urethane resin emulsion having at least one type of cationic functional group selected from the group consisting of primary to tertiary amino groups and quaternary ammonium group and/or (A-2) a non-ionic acrylic resin emulsion; a tetraalkoxysilane; at least one type of silane coupling agent having at least one type of reactive functional group selected from the group consisting of an active hydrogen-containing amino group, epoxy group, mercapto group, and methacryloxy group; a chelating agent; a vanadate compound; a titanium compound; and water; where solid content (As) of the resin emulsion with respect to the total solid content of the surface-treatment liquid is 10 to 45 mass%; solid mass ratio (C S /A S) of solid content (C S) of the silane coupling agent with respect to solid content (As) of the resin emulsion is 1.51 to 5.89; solid mass ratio (B S /D S) of solid content (B S) of the tetraalkoxysilane with respect to solid content (D S) of the chelating agent is 0.15 to 1.49; solid mass ratio (E v /D S) of content (E v) of the vanadate compound in terms of V with respect to solid content (D S) of the chelating agent is 0.03 to 0.23; and solid mass ratio (F T /D S) of content (F T) of the titanium compound in terms of Ti with respect to solid content (D S) of the chelating agent is 0.02 to 0.19; applying by coating the surface-treatment liquid to a surface of a zinc or zinc alloy coated steel sheet, and heating and drying the surface of the zinc or zinc alloy coated steel sheet to form a surface treatment coating film on the surface with a coating amount per one surface in the range of 200 to 1,000 mg/m 2. preparing a surface-treatment liquid for a zinc or zinc alloy coated steel sheet, containing following components, by blending the components in amounts, in solid mass contents calculated from respective masses of the components, which satisfy conditions to below at pH in the range of 3 to 6, the components including: a resin emulsion formed of (A-1) a cationic urethane resin emulsion having at least one type of cationic functional group selected from the group consisting of primary to tertiary amino groups and quaternary ammonium group and/or (A-2) a non-ionic acrylic resin emulsion; a tetraalkoxysilane; at least one type of silane coupling agent having at least one type of reactive functional group selected from the group consisting of an active hydrogen-containing amino group, epoxy group, mercapto group, and methacryloxy group; a chelating agent; a vanadate compound; a titanium compound; and water; where solid content (As) of the resin emulsion with respect to the total solid content of the surface-treatment liquid is 10 to 45 mass%; solid mass ratio (C S /A S) of solid content (C S) of the silane coupling agent with respect to solid content (As) of the resin emulsion is 1.51 to 5.89; solid mass ratio (B S /D S) of solid content (B S) of the tetraalkoxysilane with respect to solid content (D S) of the chelating agent is 0.15 to 1.49; solid mass ratio (E v /D S) of content (E v) of the vanadate compound in terms of V with respect to solid content (D S) of the chelating agent is 0.03 to 0.23; and solid mass ratio (F T /D S) of content (F T) of the titanium compound in terms of Ti with respect to solid content (D S) of the chelating agent is 0.02 to 0.19; solid content (As) of the resin emulsion with respect to the total solid content of the surface-treatment liquid is 10 to 45 mass%; solid mass ratio (C S /A S) of solid content (C S) of the silane coupling agent with respect to solid content (As) of the resin emulsion is 1.51 to 5.89; solid mass ratio (B S /D S) of solid content (B S) of the tetraalkoxysilane with respect to solid content (D S) of the chelating agent is 0.15 to 1.49; solid mass ratio (E v /D S) of content (E v) of the vanadate compound in terms of V with respect to solid content (D S) of the chelating agent is 0.03 to 0.23; and solid mass ratio (F T /D S) of content (F T) of the titanium compound in terms of Ti with respect to solid content (D S) of the chelating agent is 0.02 to 0.19; applying by coating the surface-treatment liquid to a surface of a zinc or zinc alloy coated steel sheet, and heating and drying the surface of the zinc or zinc alloy coated steel sheet to form a surface treatment coating film on the surface with a coating amount per one surface in the range of 200 to 1,000 mg/m 2.