PURPOSE: To effectively suppress the corrosion of a metallic surface in a water system by adding an effective quantity of a composition containing a molybdate ion source, an amine adduct of maleic anhydride, a copolymer of maleic anhydride and the like in a specified ratio into the water system.

CONSTITUTION: The molybdate ion source (a) such as Na2MoO4 and a water soluble component (b) selected from a polymaleic anhydride (amino adduct), a polymer of maleic anhydride and dimethyl diallyl ammonium chloride or the like, 50-70wt.% acrylic acid, 10-40% 2-acrylamide-2-methyl propyl sulfonic acid (polymer), 2-phosphonobutane-1,2,4-tricarboxylic acid, polyhydroxy esters or the like are incorporated in the ratio of (10:1)-(1:10) as the active component weight ratio of (a):(b). The effective quantity of the corrosion suppressing composition is added into the water system. The quantity to be added is controlled preferably to 0.1-200ppm as the weight of the active component. The effective pH is controlled to 6.0-9.0.