The tubed vortex reducer in the axial compressor can destroy the vortex in the disk cavity, by a thin-walled tube, to reduce the total pressure loss. The tube may suffer from vibration problems, such as flutter and forced vibration, which are closely related to aerodynamic damping. In this paper, the energy method and the influence coefficient method are used to study the aerodynamic damping of the tube. Based on the modal characteristics, steady and unsteady flow characteristics of the tube, the first and second modes with lower frequencies and greater vibration risk are selected as the analysis objects. The energy method is used to calculate the aerodynamic damping of the tube with different amplitudes, which shows that the results approximately meet the linear assumption and are accurate. The results obtained by the influence coefficient method show that the aerodynamic influence between adjacent tubes is very small, and the effect of inter-tube phase angle on the aerodynamic damping can be ignored. Finally, it is found that the effect of structural coupling caused by the support ring on the aerodynamic damping of the tube is mainly reflected in two aspects: frequency reduction and tube mode coupling.