A steel pipe blank having a composition containing 0.5% or less C and 85% or more Fe in terms of mass percent is heated, and stretch-reducing is then performed so that the diameter decrease ratio is 15% or more and the rolling finishing temperature is (the Ar3 transformation point−10)° C. or lower. Consequently, a structure in which the ratio of X-ray diffraction intensity obtained from the plane in which the direction of crystal grains is preferentially oriented parallel to the circumference direction and the direction of crystal grains is preferentially oriented parallel to the rolling direction of the steel pipe to that obtained for a three-dimensionally randomly oriented sample is 3.0 or more is formed, and the r-value is increased, thereby improving the magnetic properties of the steel pipe.