A polymer scale preventive agent for use in polymerization of a monomer having an ethylenically unsaturated double bond, comprising a naphthoquinone dimer compound. This agent is applied to the inner wall surfaces of a polymerization vessel to form a coating. Such a vessel is effective in preventing polymer scale deposition, not only on the areas located in the liquid-phase region but also on the areas around the interface between the gas and liquid phases in the vessel, and useful in producing a polymer that shows few fish eyes and good whiteness when formed into sheets or the like.