A polyethylene terephthalate fiber capable of being dyed under normal pressure and having an initial modulus of more than 50 g/d, a peak temperature (T max) at peak of dynamic mechanical loss tangent (tan .delta.) measured with a frequency of 110 Hz of about 85.degree. C. to about 110.degree. C., and a peak value of the dynamic mechanical loss tangent ((tan .delta.) max) of about 0.115 to about 0.135. The fiber has a sheathcore structure such that refractive indices are different between an outer layer of the fiber and an inner layer of the fiber, and a local average refractive index distributed symmetrically around the center of the cross section of the fiber. The fiber is made by extruding a dope of polyester, passing the extruded filaments through a heating zone provided at the surface of the extrusion nozzle and having a length of at least about 5 cm and a temperature of about 150.degree. C. to about the melting point of the polymer, applying a vacuum with an aspirator located below the heating zone, and then winding at a winding speed of at least about 5,000 m/min.