A coating varnish composition comprising (A) a polymer obtained by polymerizing (a) at least one unsaturated acid anhydride and (b) at least one other unsaturated monomer, and (B) at least one additive selected from triazole derivatives, benzothiazole derivatives, thiadiazole derivatives, polyethers and carboxylic acid anhydride derivatives, is capable of forming a coating which has no danger of poisoning like the organotin copolymers, shows a coating consuming property and antifouling performance comparable with those of the organotin copolymers and does not gel even when mixed with a copper compound.