Rotating holes are widely used in jet engine internal air systems as an important kind of throttling element. The flow characteristics of rotating holes are of great importance in the design of the internal air system. The aims to investigate the influence of pumping effect on the flow characteristics of axial rotating holes. Pumping effect refers to the flow phenomenon induced by a rotating plate which characterized by a radial outflow. There are altogether two types of holes considered in the paper: round hole and square hole. A 1/25 (14.4-degree) sector model is used to carry out the numerical investigation using the commercial software ANSYS CFX. In the simulation, the SST turbulent model is used. Meanwhile, a non-rotating method using the relative frame of reference is used. In the non-rotating method, an initial incidence angle is given at the inlet instead of setting the plate to be rotating, thus the pumping effect induced by the rotating plate can be eliminated. The non-rotating method results are compared with the conventional reference frame results to investigate the influence of pumping effect. The results show that due to the influence of the pumping effect-induced radial outflow, the theoretical two-dimensional incidence angle becomes three-dimensional, which has negative effects on the hole discharge coefficient. At the same time, due to a larger circumferential length, square holes will undermine the pumping effect, thus has a higher discharge coefficient than the round holes.