The hysteresis restoring force characteristic of the seismic isolation rubber has the nonlinear characteristics depending on the displacement. A method to reduce the damage of structure in the earthquake with a seismic isolation laminated rubber is discussed and the vibration characteristics of the rubber which minimize the response of the structure in earthquakes is optimized. In this research, PFT-ELS (Equivalent Linear System using the Restoring Force Model of Power Function Type : PFT-ELS) method is applied to the nonlinear vibration analysis of the rubber. And, the building model of 15 layers with the seismic isolation laminated rubber is modeled. Next, the hysteresis restoring force characteristic of the seismic isolation rubber which minimize the response of the structure in earthquakes is optimized by Genetic Algorithms (GA). As earthquakes, Kobe earthquake, the hypothetical Nankai-Tonankai-Tokai connected earthquakes and Kumamoto earthquake (16 April 2016) are used. From these results, we consider about the optimum solutions of the restoring force characteristic by different earthquakes, and we verify the availability and valuable of this optimization method. As a result, it is clarified that the vibration characteristics of the seismic isolation rubber for minimizing the damage of the structure at the design phase through developed optimization system.