Provided herein is a stainless steel seamless pipe having high strength and excellent corrosion resistance. The stainless steel seamless pipe has a composition that includes, in mass%, C: 0.06% or less, Si: 1.0% or less, P: 0.05% or less, S: 0.005% or less, Cr: more than 15.7% and 18.0% or less, Mo: 1.8% or more and 3.5% or less, Cu: 1.5% or more and 3.5% or less, Ni: 2.5% or more and 6.0% or less, Al: 0.10% or less, N: 0.10% or less, O: 0.010% or less, W: 0.5% or more and 2.0% or less, and Co: 0.01% or more and 1.5% or less, and in which C, Si, Mn, Cr, Ni, Mo, Cu, and N satisfy the predetermined formula, and the balance is Fe and incidental impurities, the stainless steel seamless pipe having a microstructure containing at least 25% martensitic phase, at most 65% ferrite phase, and at most 40% retained austenite phase by volume, and the stainless steel seamless pipe having a yield strength of 758 MPa or more.