A polymer scale preventive agent for use in polymerization of a monomer having an ethylenically unsaturated double bond, comprising an alkaline solution containing (A) a condensation product of (A-1) a hydroxynaphthalene compound and (A-2) an aldehyde compound, and (B) an inorganic colloid. This agent is used for forming a coating on the inner wall, etc. of a polymerization vessel. Such a vessel is effective in preventing polymer scale deposition, not only in the liquid-phase region but also in the vicinity of the interface between the gas and liquid phases in the vessel, and useful in producing a polymer that shows very few fish eyes and good whiteness when formed into sheets or the like.