An improved efficient uncertainty quantification (UQ) analysis framework is proposed by the combination of sparse polynomial chaos expansion (PCE) and universal Kriging (UK) metamodel to obtain the surrogate model (UK-PCE). Moreover, a challenging analytical test function and an engineering test are considered to investigate the response performance of UK-PCE method. The results show that the UK-PCE method reduces the computational cost by more than 70% in comparison to the typical PCE method. Then this method was applied to the UQ of the aerodynamic and heat transfer performance of GE-E3 rotor blade squealer tip. Additionally, a series of uncertainty quantities visualization methods based on the data mining method, parallel computing method, and Delaunay triangulation method is proposed to reveal more enlightening uncertainty phenomena in the actual operation. The results of UQ show that under the influence of uncertain inputs, the leakage flow rate and downstream entropy increase will be significantly increased. The statistical average of tip heat flux has increased by 8.56% relative to the design value, and the probability of it deviating from the design value by 10% is as high as 43.27%. In addition, the three-dimensional tip heat flux deviation distributions calculated by the proposed uncertainty quantities visualization method reveal a coupling of the hot corrosion and thermal fatigue of the squealer tip. It is also indicated that under the influence of the uncertain inputs, there is a marked increase in blade tip flux, and the blade tip flux deviation has been maintained at a high value, about 13.0%. The results of sensitivity analysis show that the largest contributor to the uncertainty of the blade tip aerodynamic performance is the tip clearance deviation and its variance index to the uncertainty of leakage flow rate and downstream entropy increase is as high as 88.21% and 62.63%. Therefore, the geometric accuracy of the tip clearance should be strictly ensured in the turbine blade assembly and marching process. The influence of the inlet total temperature deviation on the uncertainty of the heat transfer performance of the squealer tip must also be taken into account. So a satisfactory control system should be designed in the actual operation of the gas turbine to make sure that the fluctuation of inlet total temperature can be attenuated rapidly.