Tubular graphite cones (TGCs) with a single-crystal nanotip have been achieved by means of microwave plasma-assisted chemical vapor deposition using in-situ-evaporated Fe catalysts. The absence of the disorder-induced D band in Raman spectra revealed the single-crystalline feature of the nanotip. TGCs were found to stem from Fe catalytic carbon spherules on the order of 100 mu m diameter, whose critical role in promoting both nucleation and plasma annealing in the formation of highly crystalline TGCs is discussed. The crystalline quality of such TGCs can be further verified by the investigation of their oxidative stability in air. All TGCs can survive up to 600 degrees C without any structural variations, and a few TGCs still survive with an anisotropic etched and stepped nanotip at temperatures up to 800 degrees C, much better than CNTs. Thus, TGCs with single crystalline nanotips are potential candidates for scanning probes in high-temperature oxygen-containing environments.