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• Topology optimization for diffusion–reaction process in porous media is conducted. • The lattice Boltzmann method and the level-set method are coupled. • Delicately designed hierarchical porous structure are obtained. • Total reaction rate and material utilization ratio are evaluated. • Topology optimized structures overwhelm random hierarchical porous structure. Hierarchical porous media possess both high reactive sites and low transport resistance, yet the limit of the total reaction rate is not clear. In the present study, topology optimization (TO) of three-dimensional porous structures where diffusion–reaction processes occur is conducted by the lattice Boltzmann method and the level-set method to optimize the material distributions and to obtain the highest total reaction rate. Hierarchical porous structures are generated, and more mesoscopic pores are incorporated as the process gradually becomes diffusion-limited. The total reaction rate and utilization ratio of the microscopic materials are significantly improved in the TO structures. Compared with spherical structures, the TO results of spherical shell structures can significantly improve the material utilization ratio at the cost of slightly reduced total reaction rate. Finally, the TO structures are compared with random hierarchical structure, and remarkable increase of the total reaction rate is achieved. [ABSTRACT FROM AUTHOR]