In the composition of the surface-treatment agent used for metallic material, a composition having such high corrosion-resistance as to replace the chromate coating is provided. In the composition of the surface-treatment agent provided for the metallic material, fingerprint resistance, blackening resistance and adhesiveness of paint coating are also improved. The metallic material is treated by an acidic surface-treating agent comprising the following components:(A) a cationic component, which consists of divalent or higher valent metallic ions selected from the group consisting of manganese, cobalt, zinc, magnesium, nickel, iron, titanium, aluminum and zirconium;(B) at least one acid component selected from the group consisting of (1) fluoro-acid which contains four or more fluorine atoms, and one or more elements selected from the group consisting of titanium, zirconium, silicon, hafnium, aluminum and boron, (2) phosphoric acid, and (3) acetic acid;(C) a silane coupling-agent component which consists of one or more compounds which contain at least one reactive functional group selected from an amino group containing active hydrogen, an epoxy group, a vinyl group, a mercapto group and a methacryloxy group;(D) one or more water-soluble polymer components which are expressed by the following general formula (I) and has a polymerization degree of from 2 to 50 of the polymeric unit.