Blade tip clearance plays a vital role on aerodynamic performance of compressor. Slightly change of tip clearance size can result in violent change of the tip clearance flow field, and subsequently seriously affect the aerodynamic performances. Since the clearance size is subject to variabilities influenced by working conditions, manufacture, complex service process and some other factors, to improve the aerodynamic performance of tip clearance region, it is essential to study the influence of the tip clearance uncertainty on the flow field and aerodynamic performance parameters. In this paper, the tip clearance size distributions over different rotating speeds are respectively mapped. Generally, the tip clearance sizes for different working conditions satisfy the Gaussian distributions, where the mean value and standard deviation can be changed according to the conditions. Non-Intrusive Polynomial Chaos (NIPC) is introduced here to achieve the uncertainty quantification (UQ) of output aerodynamic performance parameters of compressor. The various impacts of input tip clearance size uncertainty under different working conditions are investigated here, as well as the differences and relations of these impacts on the aerodynamic Quantity of Interest (QoI). With this methodology, it is practicable to analyse the specific effects of stochastic tip clearance on compressor aerodynamic performance for different working conditions. The UQ results show that part rotating speeds conditions are more sensitive to the tip clearance size uncertainty, especially the near stall operating points. The results of this research provide some useful information to improve compressor design process and some meaningful hints for further robust design. The results shown in this paper can serve as study case for further comparisons with other UQ methodology and results as well.