Material property differences among components of solid oxide fuel cell (SOFC) lead to excessive stresses during cell fabrication and operation, among which functional gradient material electrodes have attracted attention for their ability to reduce residual and thermal stresses in SOFC. But so far, there is rare study on SOFC with functional gradient anode using numerical simulation of thermal stress. In this study, a multi-physics field coupling model of SOFC with complete structure was established by COMSOL Multiphysics 6.0. Based on multi-physics field coupling model and numerical simulation of the residual stresses and thermal stresses in SOFC, four different distribution curves were employed to characterize the component distribution of anode materials. The results show that the tensile stress of anode can be significantly reduced by using functional gradient material during fabrication at different temperatures, especially at room temperature. Compared with non-gradient distribution, the maximum tensile stress of the anode is reduced by 47.69% before reduction and 35.74% after reduction by using quadratic curve distribution. During the operation process, the heat generated by the electrochemical reaction and the convective heat transfer of gas leads to the temperature difference between inlet and outlet, resulting in significant stress concentration at inlet and outlet of the metal frame as well as at contact surface between rib and electrode. Functional gradient materials can significantly reduce the maximum stress on the anode, metal frame and electrolyte, which is particularly obvious when using quadratic curve distribution. Therefore, this research has potential theoretical significance and engineering value for designing and fabricating SOFCs.