Abstract: In the process of structural processing and manufacturing, most products inevitably exhibit certain degree of geometric uncertainties due to processing errors and other reasons, including the structural length error and uneven thickness distribution. These geometric uncertainties will cause certain performance fluctuations in the structure, leading to structural failure and posing certain safety hazards. In this paper, the geometric uncertainty of uneven thickness distribution is considered. Because the thickness distribution of the structure changes with space, it belongs to the "field uncertainty" problem. Considering the limited number of samples in the practical engineering, it is impossible to obtain the information of uncertainty probability distribution accurately, and the traditional random field method based on the probability theory is no longer applicable. Therefore, this paper proposes a non-probabilistic reliability-based topology optimization model considering the geometric uncertainty of the structure with spatial distribution characteristics based on the non-probabilistic bounded field model. In the non-probabilistic reliability-based topology optimization model, the geometric uncertainty is represented by an uncertain threshold field function, and the uncertain threshold field is described by a non-probabilistic bounded field model. The reliability-based topology optimization model is a nested optimization problem, in which the inner-loop optimization problem is used to conduct the non-probability reliability assessment of the structure, and the outer-loop optimization problem is expressed as determining the optimum topology layout of the structure based on the series expansion of material fields topology optimization method. The sensitivity information of the optimization model is obtained by the adjoint sensitivity analysis, and the gradient-based optimization algorithm based on method of moving asymptotes is used to solve the optimization problem. The differential sensitivity analysis method is used to verify the correctness of the analytical sensitivity analysis in this paper. Numerical examples are also presented to illustrate the effectiveness of the proposed non-probabilistic reliability-based topology optimization against geometric uncertainty with the bounded field model.