The aim of this research is to develop an advanced hysteresis model of High Damping Rubber (HDR) bearing. Based on the experimental research so far, various dependences and nonlinearities can be confirmed in the experimental hysteresis curves of HDR. In particular, the gap in the stiffness between the first cycle and the cycle after the second of the hysteresis curve is confirmed due to the dependence of the maximum shear strain. The advanced hysteresis model of HDR, tentatively named the bilinear Double Target model, was proposed by conducting the dynamic loading test in this research. To assess the technical feasibility of this hysteresis model, three phases were performed in this research. The preliminary proportion was carried out to confirm the mechanical behaviors of HDR by performing a dynamic loading test. Subsequently, based on the experimental results, a modeling procedure of the bilinear Double Target model was proposed and the hysteresis curve of HDR was modeled. Finally, dynamic analyses by design seismic motion are performed on the structural model of the actual bridge pier. The validity of the proposed model was confirmed by investigating the behavior of the bearing part and the lower part of the pier. As a result, it was possible to propose a hysteresis model considering the dependence of HDR and to conduct seismic response analysis.