Gradient anode is an effective way to improve the electrical performance of anode-supported solid oxide fuel cell (SOFC). However, the porosity is closely related to the thermomechanical properties and thermal stress distribution of the anode. It is thus important to investigate the comprehensive effect of porosity on the thermal stress and electrical performance of SOFC. A single planar SOFC model considering various porosity-dependent properties of the materials was proposed via multi-physics coupling based on the COMSOL Multiphysics simulation platform. The electrochemical performance and thermal stress distribution of the SOFC with a gradient–porosity-anode design at working stage were investigated. The results show that the gradient porosity-anode design effectively improves the thermomechanical matching of the positive–electrolyte–negative structure, while maintains the high electrochemical performance of the SOFC. Compared with the usual uniform porosity anode designed SOFC with a porosity of 0.4, the output power of SOFC is increased by 3.5%, while the maximum first principal stress of the electrolyte is reduced by 68.5%. The results of this study provide the theoretical and data supports for optimizing anode structure design of SOFC.