In a Zn-ion based acidic galvanizing bath containing one additive selected from the group consisting of:______________________________________ (a) Cr.sup.3.sup.+ 50 - 700ppm, (b) Cr.sup.6.sup.+ 50 - 500ppm, and (c) Cr.sup.3.sup.+ and Cr.sup.6.sup.+ 50 - 700 ppm, in which Cr.sup.6.sup.+ being 500ppm at the maximum; ______________________________________ And at least one additive selected from the group consisting of:______________________________________ (d) Sn ion 10 - 5,000ppm, and (e) In ion 10 - 3,000ppm, ______________________________________ A steel sheet is subjected to an electro-galvanizing treatment, and then, said electro-galvanized steel sheet is subjected to a conventional chromate treatment.