It is always an important research direction to improve the performance of solid oxide fuel cells (SOFCs) through structural optimization. For anode-supported SOFC, the thin cathode thickness results in an uneven distribution of oxygen concentration in the porous electrode, which limits the output performance. In this paper, a three-dimensional model of the anode-supported planar SOFC was established, and the thickness of the cathode diffusion layer in the area covered by the connector was increased to improve the uniformity of oxygen distribution in the cathode. The results show that increasing the thickness of the cathode diffusion layer under the connector can significantly improve the overall output performance of SOFC. The uniformity of oxygen concentration distribution in the cathode is improved, the local current density under the connector is increased, and the maximum output power density of the cell is increased by 29.14%. The results show that the output performance of the SOFC and the uniformity of gas distribution in the porous electrode can be improved by increasing the thickness of the cathode diffusion layer under the connector in the structure design and practical application of the SOFC. The research of this paper provides a reference for the optimization design of SOFC.