To obtain a method of manufacturing a steel pipe; wherein a special adjustment of measurements of the pipe is substantially not required for a final cold finishing working, and compressive strength in the direction of the pipe's length is more than 80% of its tensile strength even when a working parameter Q-value in the final cold finishing working is over 1.5.

Tensile strength in the longitudinal direction of the pipe shaft required for the product is given to the steel pipe in the final cold working where its diameter and thickness are reduced. When the inside diameter of the pipe before the working is designated as ID and the difference between the pipe inside diameters before and after the working is as ΔID, a processing ERD is defined as an equation 'EDR=(ΔID/ID)×100(%)'. In this case, the pipe enlarging processing with the processing degree of 0.2-5% and/or the heat treatment that the temperature is kept in the temperature range between 200 and 450°C for more than five minutes, is performed to the steel pipe.