In order to solve the problems of low-profile accuracy and poor control stability of the satellite antenna due to axial coupling vibration, in this paper, a self-resetting friction damper is proposed to suppress axial vibration. Firstly, a self-resetting friction damper, with a lightweight, wide frequency band, and high energy consumption, is designed. The principle of dry friction energy loss of metal rubber (MR) and the effect of self-resetting of shape memory alloy (SMA) are used. Secondly, the vibration reduction mechanism model of the self-resetting friction damper is established, and the principle of damping energy dissipation is analysed. Finally, sinusoidal excitation tests of the components of the satellite antennas with self-resetting friction dampers are carried out. The axial vibration loss factor of the components of the satellite antenna with the self-resetting friction damper is calculated, and the vibration resistance performance of the damper is verified. Theoretical analysis and experimental results show that the self-resetting friction damper has a significant effect on suppressing the axial vibration of the components of the satellite antenna. It is feasible to install a self-resetting friction damper in the components of the satellite antenna to suppress the axial vibration.