Recently, steel dampers are widely used as seismic reinforcement devices. Steel dampers have the advantage of being easy to manufacture and being able to absorb a lot of energy through stable hysteresis behavior. However, there is a possibility that the steel damper may be damaged due to fatigue caused by repeated seismic loads. In this study, the seismic performance of steel dampers and engineering plastic dampers with different physical characteristics were compared and analyzed. In addition, numerical analysis was performed on a hybrid damper that combines a steel damper and an engineering plastic damper. It is more effective to apply engineering plastic dampers to structures that experience significant displacement due to seismic loads. The behavior of hybrid dampers combining steel dampers and engineering plastic dampers is dominated by steel dampers. A hybrid damper in which an engineering plastic damper yields after a steel damper yields can effectively respond to various seismic loads and secure high ductility and excellent seismic performance.