To improve the brittle fracture mode of coupling beams with small span-depth ratio in RC frame-shear wall structure, a shape memory alloy (SMA) damper is installed into coupling beams in this study. The seismic performance of the structure is studied by numerical analysis. A planner 18-story frame-shear wall structure is utilized. SMA dampers are installed into coupling beams at each story. Static monotonic and cyclic loading are applied on the structure. Influence of two parameters of the coupling beam with SMA damper, the yield force ratio and the yield displacement ratio, on the nonlinear behavior of the whole structure is addressed. The analysis results indicate that the failure mode is remarkably affected by the yield force ratio. For the structures with the same yield displacement ratio, when their yield force ratio decrease, the dampers yield more early and deformation of the coupling beams is more easily to be concentrated in the dampers. At the same time, the structure has good re-centering ability. With the same yield force ratio, the increasing of yield displacement ratio results in the delay of SMA damper yielding and the concrete members damage early.