<p>The topology optimization considering stability constraints plays a crucial role in the conceptual design of structures. The parametric level set method, featuring smooth boundaries and high computational efficiency, has emerged as an innovative topology optimization approach. This paper proposes a non-probabilistic reliability-based topology optimization scheme for continuum structures based on the parametric level set method with stability constraints. The scheme obtains continuous sensitivity information through finite element linear buckling analysis and processes high-order eigenvalues via the aggregation function method. By integrating the parametric level set method, a non-probabilistic reliability topology optimization framework with buckling performance constraints is established. Furthermore, considering uncertainties in material parameters, loads, and other factors in engineering practice, the interval vertex matching point method and polynomial response surface surrogate model are adopted for uncertainty propagation analysis. The uncertainties are transformed into non-probabilistic reliability indices based on characteristic distances, ultimately developing a non-probabilistic reliability topology optimization method considering buckling responses. Finally, numerical examples demonstrate the differential characteristics of structural topology optimization under the influence of different uncertain factors.</p>