For the uncertainty analysis of aeronautical structures, it is common for input parameters to exhibit sparsity due to the limitations of experimental costs. This paper proposes an uncertainty analysis approach for aeronautical structures with sparse experimental data. A Gaussian Process Regression (GPR)-based surrogate modeling approach is developed, integrating an augmented input space to compensate for limited test samples. The augmented space generates supplementary training data through iterative expansion, enabling continuous refinement of the GPR model to establish accurate variable-response mappings. A nested Monte Carlo sampling strategy propagates probability box (P-box) parameters until response boundaries converge. The proposed method is validated through a numerical case and an aeronautical structural application. Subsequently, it is implemented for uncertainty analysis of breaking strength in civil aircraft fuse pins, with comparative studies conducted against two traditional engineering method. The framework effectively addresses uncertainty propagation challenges without requiring additional physical tests, offering enhanced computational efficiency for safety–critical structural assessments. Key innovations include the adaptive augmented space mechanism and convergence-driven P-box boundary determination, which collectively advance sparse-data uncertainty analysis in aerospace engineering applications.