The steel pipe has a structure composed mainly of ferrite or ferrite plus pearlite or ferrite plus cementite. The steel pipe is characterized by grain size not greater than 3 &mgr;m, preferably not greater than 1 &mgr;m, elongation greater than 20%, tensile strength (TS:MPa) and elongation (E1:%) whose product is greater than 10000, and percent ductile fracture greater than 95%, preferably 100%, measured by Charpy impact test on an actual pipe at −100° C. The structure is characterized by C: 0.005-0.03%, Si: 0.01-3.0%, Mn: 0.01-2.0%, and Al: 0.001-0.10% on a weight basis, and is composed of ferrite or ferrite and a secondary phase, with ferrite grains being not greater than 3 &mgr;m and the secondary phase having an areal ratio not more than 30%. A steel pipe stock having the above-mentioned composition is heated at a temperature of (Ac1+50° C.) to 400° C. and subsequently reduced at a rolling temperature of (Ac1+50° C.) to 400° C. such that the cumulative reduction of diameter is greater than 20%. The reducing is preferably performed such that at least one of rolling passes reduces the diameter by more than 6% per pass. The steel pipe will have high ductility and high strength and will be superior in toughness and stress corrosion cracking resistance, if the content of C, Si, Mn, and other alloying elements is limited low and reducing is performed at the temperature specified above. The resulting steel pipe has good fatigue resistance and is suitable for use as line pipe.