To provide a method for continuously polymerizing a polyarylene sulfide (PAS) effective for improvement and stabilization of a molecular weight by establishing a method by which the attachment of the polymer to a polymerization vessel is prevented, and a polymer phase and a solvent phase can be discharged at a constant ratio from the polymerization vessel thereby, as a result, to keep the PAS composition (concentration) in the polymerization vessel constant always.

The method for continuously producing the polyarylene sulfide by reacting a sulfur source with a dihalogenated aromatic compound in an aprotonic organic solvent includes at least one polymerization step in which the phase is separated to two phases of a polymer phase and a solvent phase and the polymer phase of a disperse phase is in a spherical droplet shape. A terminal stopper is used in the polymerization step.