Brush seals are widely applied in turbomachinery to control leakage flow between the stationary and rotational components due to the high sealing performance. In consideration of the axial compression of the bristle pack posing a challenge to accurately predict the leakage flow rate at the practical operating condition, the 3D staggered tube bundle model is established based on the multi-block structured mesh. The mesh motion technique is used to obtain the leakage flow pattern and aerodynamic resistance performance of the brush seal. The effects of pressure ratio Rp, sealing clearance c and axial pitch reduction ΔSx,i on leakage flow characteristics as well as Eu of the brush seal were investigated. The numerical results were in good agreement with the experimental data. Thus the accuracy of the presented numerical method was validated. For the contacting brush seal, ΔSx,i has a significant effect on the leakage flow rate reduction. As the ΔSx,i increases from 0 mm to 0.004 mm, the leakage flow rate is reduced by 39.63% when Rp equals to 1.5. For the clearance brush seal, ΔSx,i has little effect on the leakage flow rate reduction. As the ΔSx,i increases from 0 mm to 0.004 mm, the leakage flow rate is reduced by 3.44% when Rp equals to 1.5 and c equals to 0.2 mm. As for the aerodynamic resistance, the presence of the sealing clearance could effectively convert the pressure energy of the leakage flow into kinetic energy. This causes that the leakage flow velocity exiting the bristle pack of the clearance brush seal is 1.5 to 2.0 times than that of the contacting brush seal. Although the existence of the sealing clearance obviously increases the leakage flow rate, it effectively reduces the aerodynamic forces acting on the bristles. This research would provide technical support for the analysis of the leakage flow characteristics of the brush seal.