In order to reduce the damage of the coupling beams in the coupled reinforced concrete shear wall structure under strong earthquake, realizing the rapid recovery of the structural function after earthquake, a new hybrid damping coupling beam with self-centering and energy dissipation functions were proposed. An innovative composite self-centering damper composed of shape memory alloy strands and viscoelastic damping devices was installed in the middle span of the innovative self-centering energy-dissipating coupling beam. A 10-layer coupled shear wall structure was taken as an example. The dynamic time history analysis on the coupled shear walls with the innovative self-centering damper, viscoelastic damper and common RC coupling beam, respectively, were conducted to investigate the seismic response mitigation effect of different damper on the shear wall structure. The calculation results show that the deformation and energy dissipation of the structure are concentrated on the coupling beam damper under the actions of earthquake, while the new self-centering coupling beam damper has better control effect than the viscoelastic damper for the seismic response of the structure, exhibiting excellent re-centering and energy dissipation capacities during the earthquakes.