Melt-spun polyester fibers are taken up in the absence of heat at a speed of 5,000 to 6,000 m/min under conditions that satisfy the following relations (IX) and (X), subsequently heat-treating the fibers for a period of from 0.01 to 0.05 seconds with a heating roller while the length of the melt-spun fibers is held constant with no drawing step being provided between the taking up and heat treatment steps, and finally winding up the heated fibers0.04.ltoreq.L/(SSxd).ltoreq.0.08 (IX)1.0.ltoreq.To.ltoreq.1.5 (X)where L is the distance (cm) between the spinneret and the convergence point, SS is the speed (m/min) of a take up roller, To is the spinning tension (g/d) at a point immediately after the convergence point and D is the filament fineness (d) of the fiber wound up and is within the range of from 1 to 3 d.