It is important to accurately estimate the impact of manufacturing geometric variations on the turbine aerodynamic performance for the engineering design and manufacture. In this paper, a method to quantify the uncertainty impact of the blade geometric variations was proposed. The principal-component analysis combined with the Kolmogorov-Sminov test and the Sobol sensitivity analysis was used for the uncertainty modeling of the blade geometric variations, and the Kriging surrogate model based on the polynomial chaos expansion (PC-Kriging) was used for the uncertainty quantification in the method. Meanwhile, a Reynolds Average Navier-Stokes (RANS) solver was combined to simulate the aerodynamic performance. This method was applied to estimate the impact on the aerodynamic performance of a low-pressure turbine. The calculation results demonstrated that the aerodynamic performance was significantly influenced, which was manifested as an overall deterioration, a large fluctuation and several extreme cases. Detailed analysis of the mechanisms at the origin of the variations in the aerodynamic performance indicated that the variations of total pressure loss mainly come from the variations of the wake mixing loss, and the 70%-100% axial region on the blade is the sensitive region. The geometric variations, especially the variations of the blade thickness, in the sensitive region are one of the main factors leading to the performance variations. In the engineering manufacture, reasonable formulation of the manufacturing tolerance based on the results of the uncertainty analysis can improve the turbine aerodynamic performance under the influence of the geometric variations. (C) 2019 The Authors. Published by Elsevier Ltd.