With the continuous increase of aerodynamic and thermal load, the endwall of modern gas turbines has become the critical region affected by the uncertainties in the manufacturing and operation process and thus is very likely to suffer performance degradation and thermal failure. Therefore, it is critical to understand and quantify the impacts of uncertainty factors on endwall aero-thermal performance. Based on Kriging surrogate, the frameworks of uncertainty quantification and global sensitivity analysis are constructed for a gas turbine blade endwall. The impacts of slot geometry deviations (slot width, endwall misalignment) and mainstream condition fluctuations (turbulence intensity, inlet flow angle) on endwall aero-thermal performance are quantified and analyzed. Results show that the actual performance of the endwall has a high probability of deviating from its nominal value. With respect to the nominal values, the maximum deviations of aerodynamic losses, averaged film cooling effectiveness and averaged Nusselt number reach up to 0.33%, 45% and 5.0%, respectively. The critical regions which are most sensitive to the input uncertainty parameters are identified. Furthermore, the inlet flow angle is proved to be the most significant parameter affecting the endwall aero-thermal performance through sensitivity analysis. The influence mechanisms of the inlet flow angle on endwall aero-thermal performance are clarified by detailed flow and thermal field analysis. Results show that the inlet flow angle significantly alters the size and strength of the secondary flow structures, resulting in a large variation of endwall aero-thermal performance. Quantitatively, a positive incidence angle of 2 degrees can lead to a 0.1% reduction of total pressure coefficient, a 12% reduction of averaged film cooling effectiveness and a 2% enhancement of averaged Nusselt number.