An improved process for producing a polymer by polymerizing a monomer having an ethylenic double bond in a polymerization vessel having a polymer scale preventive coating film on its inner wall surfaces, etc. is provided. The coating film is formed by coating a first coating liquid containing a compound selected from the group consisting of an aromatic compound having 5 or more conjugated .pi. bonds and a heterocyclic compound having 5 or more conjugated .pi. bonds, and then coating a second coating liquid on the first layer. The first and second coating liquids are applied by means of steam as a carrier. The second layer has a surface having a contact angle to water of less than 60.degree. after its surface has been brought into contact with a solution of mixture of water and a vinyl chloride monomer in a weight ratio of 1:1, at 50.degree. C. for 1 hour. This process can shorten the time for forming the coating film to improve productivity, can improve the effect of preventing adhesion of polymer scale, can make colored particles less mix into polymer products obtained by this process, can lessen fish eyes and initial discoloring of formed products and can improve the quality of polymeric products and their formed or molded products.