A process for stainless-steel pipe production which comprises piercing rolling a raw material stainless steel containing, by mass, Cr: 10-30%, to give a hollow shell, elongating rolling the hollow shell using a mandrel bar, together with a graphite-free lubricant, to give a finishing rolling blank pipe and heating the blank pipe in a reheating furnace and subjecting the same to finishing rolling by sizing rolling to produce a hot-finished pipe, and then subjecting this pipe as a mother pipe to cold working to produce a stainless-steel pipe. In the reheating furnace, the finishing rolling blank pipe is heated to 1000° C. or more and subjected to heating in which an oxidizing gas is blown into the pipe inside, whereby a stainless-steel pipe which is inhibited from forming a carburized layer in the pipe inner surface can be produced. When the finishing rolling by sizing rolling to give a cold working mother pipe is carried out by stretch reducer rolling at 860-1050° C., an annealing heat treatment of the mother pipe for cold working can be omitted. Thus, a stainless-steel pipe having excellent surface quality can be efficiently produced.