A para-phenylene sulfide block copolymer consisting essentially of a recurring unit (A) ##STR1## and a recurring unit (B) ##STR2## said recurring units (A) being present in the form of a block of 20 to 5,000 units of (A) on the average in the molecular chain, the mol fraction of the recurring units (A) being in the range of 0.50 to 0.98, the block copolymer having a melt viscosity (.eta.*) of 50 to 100,000 poise as determined at 310.degree. C. at a shear rate of 200 sec.sup.-1 and having: (a) a glass transition temperature (Tg) of 20.degree. to 80.degree. C., (b) a crystalline melting point (Tm) of 250.degree. to 285.degree. C., and (c) a crystallization index (Ci) of 15 to 45, this value being that of the heat-treated, but not stretch-oriented copolymer, which block copolymer is preferably produced by a process comprising a first step of heating an aprotic polar organic solvent containing a dihaloaromatic compound consisting essentially of a m-dihalobenzene and an alkali metal sulfide to form a reaction liquid (e) containing a m-phenylene sulfide polymer consisting essentially of recurring units (B) ##STR3## and a second step of adding a p-dihalobenzene to the reaction liquid (E) and heating the mixture in the presence of an alkali metal sulfide an an aprotic polar organic solvent to form a block copolymer consisting essentially of the recurring units (B) and recurring units (A) ##STR4##