A steel pipe is produced by a method including performing diameter-reducing rolling on a steel pipe in a temperature range of from 600° C. to Ac3 with a reduction in diameter of not less than 30%, preferably after heating the steel pipe to temperatures of not lower than Ac1, the steel pipe being produced by seam-welding strip steel, or a method further including the step of performing heat treatment of holding the rolled steel pipe in a temperature range of from 600° C. to 900° C. for a time of 1 second or longer during cooling subsequent to the diameter-reducing rolling or by reheating the rolled steel pipe after the cooling.