A three-dimensional model of anode-supported planar solid oxide fuel cells (SOFCs) was developed. The output performance, temperature distribution, and concentration distribution of a SOFC stack were studied when the pitch width and rib width on the anode side of the SOFC model were different from those on the cathode side. The results showed that under the same voltage, SOFC performance can be improved by using a smaller connector rib width on the cathode side than on the anode side, and the output power can be increased by 24%. It was also found that under the same conditions, the larger pitch width of the connector on the anode side and the smaller pitch width on the cathode side could improve the output performance of SOFCs. The research provides a reference for the design optimization of SOFC stacks.