By avoiding a phenomenon that an outer surface of a parison and an inner surface of a chuck rub against each other upon contact of the chuck with the parison as well as a phenomenon that accumulations of parison are formed on the chuck immediately after gripping of the parison by the chuck, there is provided a blow molding capable of maintaining the parison thickness distribution uniform, fabricating high-quality molded products, and improving its productivity. Disclosed is a parison supply device 1 for supplying, to a blow mold, a parison discharged from an extrusion die, the parison supply device 1 including: a pair of chucks 2 for pinching, from above and below, a parison P discharged downward from the extrusion die 10; and a chuck operation part 3 for controlling an operation of pinching the parison P by the pair of chucks 2 and an operation of moving the pair of chucks 2. By the chuck operation part 3, the pair of chucks 2 performs the operation of pinching the parison P while being moved downward.