This study proposes an RCS composite damping device that can achieve seismic reinforcement of existing buildings by dissipating energy by inelastic deformation. A series of experiments assessing the performances of the rubber core pad, hysteretic steel slit damping device, and hybrid RCS damping device were conducted. The results showed that the ratios of the deviations to the mean values satisfied the domestic damping-device conformity condition for the load at maximum device displacement in each direction, at the maximum force and minimum force at zero displacement, as well as the hysteresis curve area. In addition, three analysis models based on load-displacement characteristics were proposed for application to seismic reinforcement design. In addition, the validity of the three proposed models was confirmed, as they simulated the experimental results well. Meanwhile, as the shear deformation of the rubber-core pad increased, the hysteretic behavior of super-elasticity greatly increased the horizontal force of the damping device. Therefore, limiting the allowable displacement during design is deemed to be necessary.