A graded anode-supported solid oxide fuel cell (SOFC) with the structure porous Ni-yttria stabilized zirconia (Ni-YSZ)vertical bar microporous Ni-YSZ vertical bar YSZ vertical bar La0.8Sr0.2MnO3 (LSM) was fabricated by a trilayer co-pressing-sintering method, and coating with an LSM cathode. Cu-CeO2 was impregnated into the porous Ni-YSZ layer using nitrate/glycol precursors to act as an anti-carbon catalyst to fabricate a graded Cu-CeO2-NiO-YSZ composite anode. The current-voltage (I-V), current-power (I-P), and long-term stability of the SOFC were tested using CH4 or H-2 as fuels and air as an oxidant. The results show that the co-pressing-sintering layers possess a gradient pore structure with defect-free combination. The power density of SOFC supported by a graded Ni-YSZ anode is 284 mW.cm(-2), operated at 850 degrees C using H-2 as a fuel, but decreases to 143 mW.cm(-2) when the fuel is changed to CH4. In contrast, the cell supported by a Cu-CeO2-Ni-YSZ anode show the reverse behavior, increasing from 176 to 196 mW.cm(-2) when the fuel is changed from H-2 to CH4 at 850 degrees C. Under a 250 mA.cm(-2) load using CH4 as the fuel, the output of the cell with a graded Ni-YSZ anode fluctuats and the cell is blocked after 10 h. At this point, carbon particles or fibers are observed in the anode layer by scanning electron microscopy (SEM). Conversely, the cell with a Cu-CeO2-Ni-YSZ anode shows stable power output for 50 h or longer, and no carbon deposition was observed inside the anode.