Buckling failure is a critical failure mode of thin-walled stiffened structures and severely limits their load-carrying capacity. To enhance buckling strength, previous studies have introduced the concept of hierarchical stiffened structures. Motivated by this idea, this paper investigates the density-based topology optimization method for designing hierarchical thin-walled stiffened structures. The proposed hierarchical model consists of stiffeners at two distinct scales: at the macroscale, stiffeners are modeled as relatively tall solid structures, while at the microscale, stiffeners are modeled by shorter graded lattice structures. The hierarchical structure is formulated by extending the multi-material interpolation scheme, in which the lattice structure is treated as an additional material phase whose geometric size can be adjusted through the size parameters. Within this framework, the extrusion constraint and casting constraint are imposed on the density fields of the macroscopic and microscopic stiffeners, respectively, enabling effective control of the stiffener height distribution. The topology optimization formulation is then defined to minimize the compliance subject to volume and buckling constraints. Finally, a four-corner simply supported plate is investigated as a numerical example to validate the proposed method. The results demonstrate that, the optimized hierarchical stiffened structures exhibit a significant improvement in buckling strength compared with conventional single-scale stiffened structures.