Disclosed herein is a process for producing a medium- or high-molecular-weight polyarylene sulfide which comprises subjecting an alkali metal sulfide, a dihalo aromatic compound and optionally, small amount of tri- or higher polyhalo aromatic compound to dehalogenation and sulfidation reaction at a temperature of from 240.degree. to 270.degree. C. in the presence of a water in amount of from 0.5 to 5 mol per 1 kg of an aprotic organic polar solvent until the conversion of said dihalo aromatic compound reaches from 70 to 98 mol %, thereby forming a polyarylene sulfide prepolymer having a melt viscosity of from 5 to 300 poise (as measured at 310.degree. C. under a shear rate of 200 sec.sup.-1), adding water to the resultant reaction mixture containing the polyarylene sulfide prepolymer so that from 6 to 15 mol of water is present per 1 kg of said solvent, and then continuing the reaction at a temperature of from 240.degree.-290.degree. C., in which the reaction comprising said two steps is conducted for from 2 to 6 hours.