A process for producing a polymer by polymerizing in a polymerization vessel a monomer having an ethylenic double bond is provided. In this process, the polymerization vessel has a polymer scale preventive coating film on its inner wall surfaces and other surfaces with which the monomer comes into contact during polymerization. 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 {character pullout} bonds and a heterocyclic compound having 5 or more conjugated {character pullout} bonds and a second coating liquid containing at least one hydrophilic compound selected from the group consisting of a water-soluble polymeric compound, an inorganic colloid, an inorganic salt and an acid; the first coating liquid and the second coating liquid being simultaneously coated by means of steam as a carrier. This process can shorten the time for forming coating films of scale preventive agents to improve productivity, can improve the effect of preventing scales, 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.