In this paper, an anode and cathode material scheme with a continuous gradient variation of components is presented. The residual stress distribution of each part of the electrode model under the new material structure is derived by calculating the residual stress during the sintering process, and the optimal material component distribution curve is derived from the analysis of the results. A multi-physics 3D model covering heat transfer, mass transfer, flow, electrochemistry and solid mechanics is developed with the help of the finite element analysis software COMSOL Multiphysics 5.5. Simulation experiments are conducted to verify the effectiveness of the method for mitigating thermal stress mismatch, reducing residual stresses and increasing the working life of the fuel cell. The results show that the use of functional gradient materials for one side electrode significantly reduces the residual stresses generated in the other side electrode during sintering, and the effect of the sinusoidal distribution curve is the most significant. The stress concentration at the electrode-electrolyte interface can be improved when both side electrodes are used with functional gradient materials at the same time, and the sinusoidal and primary linear distributions are more effective.