To avoid the proneness to degradation due to coking in the operation of solid oxide fuel cells (SOFCs) directly running on methane (CH4) fuels, a modified porous anode of the Ni1−XCoX/YSZ (yttria-stabilized zirconia) cermet prepared by an impregnation method is presented. The influence of the Co alloying content on the cermet microstructure, SOFC characteristics, and prolonged cell performance stability has been studied. Co was incorporated into Ni and formed a solid solution of Ni1−XCoX alloy connected with the YSZ as the cermet anode. The porous microstructure of the Ni1−XCoX/YSZ cermet anode formed by sintering exhibited a grain growth with an increase in the Co alloying content. The electrochemical performance of the cells consisting of the Ni1−XCoX/YSZ cermet anode, the YSZ electrolyte, and the LSM (La0.8Sr0.2MnO3) cathode showed an enhancement by the Ni1−XCoX impregnation treatment for the respective supply of H2 and CH4 to the anode. The cell using the Ni0.75Co0.25/YSZ cermet anode (the Ni0.75Co0.25 cell) showed the highest cell performance among the cells tested. In particular, the performance enhancement of this cell was found to be more significant for CH4 than that for H2; a 45% increase in the maximum power density for CH4 and a 17% increase for H2 at 750 °C compared with the performance of the cell using the Ni/YSZ cermet anode. Furthermore, the prolonged cell performance stability with a continuous CH4 supply was found for the Ni0.85Co0.15 and Ni0.75Co0.25 cells at least for 60 h at 750 °C. These enhancement effects were caused by the optimum porous microstructure of the cermet anode with the low anodic polarization resistance.