<p>This paper considers a non-probabilistic reliability topology optimization method of continuum structures under uncertainty. To do this, we first propose an evolutionary topology optimization algorithm that represents the smooth boundary using a level set function updated by the nodal sensitivity numbers. Next, we propose a two-step search-based structural non-probabilistic reliability analysis method to improve convergence performance and computational efficiency while ensuring the accuracy of the structural non-probabilistic reliability analysis for highly nonlinear problems. Combining the proposed evolutionary topology optimization method and the two-step search-based non-probabilistic reliability analysis method, an algorithm for solving the topology optimization problem of continuum structures formulated with volume minimization under reliability constraints expressed as displacements is constructed, and the accuracy and effectiveness of the proposed method are verified through numerical calculation for typical problems. Numerical results show that the proposed non-probabilistic reliability topology optimization method based on the level set model is an effective method to solve efficiently the reliability topology optimization problem of continuum structures with smooth representation of the boundary shape.</p>