Abstract: To meet the requirements of multi-functional structures for the integration of load-bearing and heat dissipation,a topology optimization design method for functionally graded cellular structures is proposed.The C0 continuous graded cellular structure modeling is realized firstly based on the triply periodic minimal surface.The numerical homogenization method is then applied to calculate the macroscopic equivalent elastic tensor and thermal conductivity tensor of cellular structures.Finally,the volume fraction of the cellular structures is used as the design variables to establish a weighted multi-objective topology optimization model to minimize structural compliance and optimize thermal conduction efficiency.The model is then solved by the optimality criteria method.Numerical results show that compared with the single-objective topology optimization design,this method sacrifices lower heat dissipation performance to obtain higher load-bearing performance,which significantly improves the overall performance of the cellular structure.