<p>In damage analysis, the simultaneous presence of random and interval variables poses significant challenges for structural damage assessment. To address this issue, an efficient hybrid uncertainty quantification framework is proposed. In simulations, the gradient-enhanced non-local damage model is utilized to avoid mesh dependence, and the Hermite polynomial chaos expansion model is adopted to approximate the results of the finite element method. To further enhance the efficiency of uncertainty analysis, the Clenshaw–Curtis collocation method and the Smolyak algorithm are employed. With regard to hybrid uncertainty analysis, a hybrid uncertainty method based on the modified chaos control method and the multiplicative dimensionality reduction method is proposed. Three numerical examples are carried out to verify the accuracy and efficiency of the proposed method, and the results demonstrate that the computational cost can be remarkably reduced while maintaining sufficient precision. The proposed method offers a simple and efficient computational framework for non-local damage analysis under hybrid uncertainties.</p>