Abstract: Centrifugal pumps have been widely used in the national economy and defense industry. Their hydraulic performance can depend mainly on the geometric parameters (such as blade angle, blade wrap angle, impeller outlet width, and blade inlet edge) and operating conditions (such as rotation speed and flow rate). Among them, the fluctuation of the inlet flow velocity over time has posed a great impact on the hydraulic performance of the centrifugal pumps during operation. This study aims to quantify the uncertain perturbation of the inlet flow velocity using the non-intrusive polynomial chaos (NIPC). A systematic investigation was implemented to explore the effect of the perturbation on the hydraulic performance of centrifugal pumps. The results show that the random inflow velocity shared a significant impact on the hydraulic performance of the pump. Specifically, the greater the uncertainty was, the greater the impact was. There was a larger difference between the mean and original pressure distribution, as the uncertainty increased, indicating a more significant impact on the pressure distribution on the blade surface. At the same time, there was a much greater distribution of pressure coefficient on the blade pressure surface under velocity disturbance deviates from the original design, as the flow rate increased. Therefore, the impact of inlet flow velocity disturbance on the blade pressure surface was significantly larger under design and high flow rate than that under the low one. Once the uncertainty was 1% and 5%, the disturbance of inlet flow velocity caused significant vibrations in the pressure and velocity near the blade suction surface, while there was a relatively small impact on the flow field near the blade pressure surface and the impeller outlet. The fluctuation range was large when the uncertainty increased to 10%. The variation of the inlet flow velocity also caused significant fluctuations in the pressure of the impeller outlet, resulting in certain variations in the pump head and efficiency. Meanwhile, there was the asymmetric and non-uniform propagation of the inflow uncertainty in the internal flow field of the impeller. There was also the variation in the impact of inflow velocity disturbance over time on pump performance under different operating conditions. In addition, the disturbance of the inflow velocity under most operating conditions caused to decrease in the pump performance. Particularly, the head and efficiency decreased by 0.4 m and 3%, respectively, when the uncertainty was 5%. There was also a decrease in the head and efficiency of the pump under design conditions, compared with the reference model. But there were relatively small decreased values and the range of variation when the uncertainty was 1%. Furthermore, the head and efficiency of the pump increased at 0.2Q_d in the design condition, compared with the reference model. Both absolute values of the mean and standard deviation were larger than before. The quantitative analysis of the uncertain inlet flow velocity can evaluate the robustness of the centrifugal pump under the whole operating conditions.