The production method of the present invention includes: a supplying step of supplying reaction raw materials to at least one of a plurality of reaction vessels mutually communicated through a gas phase; a polymerizing step of carrying out a polymerization reaction; and a step of removing at least some of the water present in the reaction vessels. Each of the steps is carried out in parallel, and a reaction mixture is transferred sequentially between the reaction vessels. The total amount of water contained in the reaction raw materials in at least one of the reaction vessels to which the reaction raw materials are supplied is 3 moles or more per mole of the sulfur source, and the internal temperature of at least one of the reaction vessels to which the reaction raw materials are supplied is from 180° C. to 300° C.