The present invention discloses a process for producing a granular polyarylene sulfide which has a high melt viscosity and a high degree of cross-linkage, becomes gel under melting and is easy to handle in the production and the fabrication thereof.The process disclosed herein comprises (1) a step (A) an initial-stage polymerization step for obtaining a polyarylene sulfide by reacting an alkali metal sulfide, a dihaloaromatic compound and a polyhaloaromatic compound, having three or more halogen substituents in a molecule, in the presence of water in an amount of 0.5 to 2.9 moles per mol of said alkali metal sulfide at a temperature in the range of 180.degree. to 235.degree. C. until the total conversion ratio of said dihalo- and polyhaloaromatic compounds reaches 50 to 98% and the melt viscosity of a polyarylene sulfide obtained at the end of the step becomes 5 to 5,000 poise, measured at 310.degree. C. and a shear rate of 1,200/second; (2) a step (B) a temperature raising step in which while adjusting an amount of water to be 2.5 to 7 moles per mol of fed alkali metal sulfide, a temperature raising condition from the temperature of step (A) to 240.degree. C. is controlled so that the melt viscosity of a polymer obtained at 240.degree. C. reaches 300 to 10,000 poise, measured at 310.degree. C. and a shear rate of 1,200/second and the temperature raising rate between 240.degree. C. and a temperature of the following step (C) is further controlled to be within the range of 10.degree. to 100.degree. C./hour; and (3) a step (C) a second-stage polymerization step for further continuing the reaction at a temperature of 245.degree. to 290.degree. C. until a melt viscosity of the final product reaches not lower than 1.times.10.sup.5 poise, measured at 330.degree. C. and a shear rate of 2/second.The present invention also discloses a granular cross-linked polyarylene sulfide produced by the process described above.