To provide a condition of melt extrusion under which the spinning of a polyester produced by a microorganism, which conventionally has a problem in the spinning stability, can be stably carried out, and not only P(3HB) and P(3HB-CO-3HV) but also P(3HB-CO-3HH) can be smoothly spun, and further to provide a drawing method to provide a filament having characteristic properties.

A thermoplastic polymer is extruded from a melt extruder, and rapidly cooled to the temperature lower than the glass transition temperature just after the extrusion to protect the obtained filament from blocking, and the cooled filament is allowed to be rapidly and partially crystallized at the temperature higher than the glass transition point to provide the objective biodegradable fiber.