To enable the removal, as much as possible, of the influence of the change of the properties of polyester undrawn yarns caused by the laps of time depending on leaving conditions when the yarns are kept in a can containing water in an amount of 20% or more for a long time, the obtaining of polyester yarns having drawing property and shrinking property similar to the yarns obtained from the undrawn yarns directly after spinning, and the production of highly shrunk yarns of polyester fibers under stable conditions.

When undrawn yarns of polyester fiber are drawn in bath liquid, the primary drawing is carried out in a bath liquid of 65°C or less at a drawing ratio of 1.2-1.5, subsequently the secondary drawing is carried out at a drawing ratio of 1.0-1.8 in the bath liquid warmed up to 75-95°C, and successively the remaining drawing, that is, the tertiary drawing is carried out at a temperature of 55-75°C and lower than the temperature of the secondary drawing by 5°C or more.