an object of the present invention is to provide a reasonable polycondensation step by which an appropriate molecular weight can be obtained and material decomposition associated with thermolysis can be suppressed , so as to contribute to production technology for ptt polymers . the production method for polytrimethylene terephthalate comprises an esterification step and a polycondensation step , wherein the polycondensation step is divided into multiple stages , polycondensation is performed using a polymerization vessel having a twin - shaft agitator in the final stage of the polycondensation step , and the polymerization temperature during the subsequent stage of the polycondensation step is less than the polymerization temperature during the former stage of the polycondensation step .