A chemically stable perovskite material Sr2Fe1.5Mo0.5O6 (SFMO) is employed as the anode of a solid oxide fuel cell (SOFC). An electrolyte-supported single cell with anode, electrolyte and cathode all made of perovskite structured materials and with a configuration of SFMO|La0.8Sr0.2Ga0.83Mg0.17O3|Ba0.5Sr0.5Co0.8Fe0.2O3 (SFM|LSGM|BSCF) is fabricated by a screen printing method. The single cell gives a maximum power density of 391 mW cm−2 for CH3OH, and 520 mW cm−2 for H2 as the fuel, respectively, at 1073 K with oxygen as the oxidant gas. The mass spectra of the flue gas out of the test reactor confirm that methanol thermally decomposes inside the anode chamber and generates mainly CO and H2 at 1023 K. Analysis of the after-test cell tells that the anode surface has no carbon formation under reaction with methanol as the feed for 3 h. The carbon resistance is attributed to the fact that the anode is in oxide state which cannot facilitate the formation of bulk carbon with graphite structure. The fast activation and gasification of the carbon species by the oxidative atmosphere around the anode surface are also beneficial factors. The test results indicate also that the activation of CH3OH is much more difficult than that of H2.