To produce a polystyrene resin with high productivity which is not in the former whereby the increase of molecular weight is enough possible, high quality and good moldability are obtained and especially the suitability as a molding material for foamed sheet and foamed molded product is obtained.

The method produces the polystyrene resin of which the weight average molecular weight is 200,000 to 700,000 and the ratio (Mw/Mn) of the weight average molecular weight(Mw) to the number average molecular weight(Mn) is 3.0 or less by using an organic peroxide represented by formula (1) (wherein R1, R2, R3 and R4, which may be the same or different, are each a group of formula (2) (wherein X is an integer of 0 to 3; Y is a tertiary alkyl group or tertiary aralkyl group)) as a polymerization initiator and performing the polymerization of a styrene monomer or a polymerizable composition having the monomer as a principal component.