A parison supply device that continuously supplies, to a blow molding die, parison sections of a parison discharged from an extrusion die, the parison section having a specified length. The parison supply device includes a plurality of tension chucks and a tension chuck operation unit that operates the plurality of tension chucks. The tension chuck operation unit causes the individual tension chucks to perform a repeated operation of grasping the parison at a first position near the extrusion die and moving to a second position separated from the extrusion die such that, before the preceding tension chuck is separated by a set distance from the extrusion die at the second position, the following tension chuck grasps the parison at the first position, and then the parison section is supplied to the blow molding die.