A stainless steel pipe is provided by a method including performing diameter-reducing rolling on a steel pipe in a temperature from 600° C. to Ac3 with a reduction in diameter of 30% or higher. Preferably, after heating the steel pipe to temperatures of not lower than Ac1, the steel pipe being produced by seam-welding strip steel includes the step of performing heat treatment to hold the rolled steel pipe in a temperature from 600° C. to 900° C. for at least 1 second during cooling subsequent to the diameter-reducing rolling or by reheating the rolled steel pipe after cooling.