Abstract: To address the issue that traditional deterministic topology optimization may generate stress concentration-sensitive structures under load uncertainty, this paper proposes a robust topology optimization (RTO) method for structural stress based on a velocity field level set framework. By employing the Polynomial Chaos Expansion (PCE) method, a stochastic response surrogate model for maximum structural stress under load uncertainty is developed. The mean and standard deviation of stress are directly extracted from the PCE expansion coefficients, establishing a robustness-oriented topology optimization model that minimizes their linear combination. The velocity field level set method is adopted for topological evolution, where analytical sensitivities of the statistical moments of global maxi-mum stress with respect to velocity design variables are derived by integrating direct differentiation and adjoint variable methods. The Globally Convergent Method of Moving Asymptotes (GCMMA) is introduced to ensure stable updates of design variables. Finally, two numerical examples and Monte Carlo Simulation (MCS) validate the effect-iveness and stability of the proposed method. The influences of weight coefficients in the objective function, the coefficient of variation of stochastic loads, and volume constraint limits on the optimization results are also discussed.