This study is concerned with the active vibration control of cranes against earthquake induced vibration. For this purpose, Linear Matrix Inequalities (LMIs) based actuator saturated mixed H-2/H-infinity state-feedback controller is designed in this paper. Performance of the designed controller and active vibration control system is investigated by simulation. The time history of ground motion of the Marmara Kocaeli earthquake, which is a disturbance input, is applied to modeled container crane. Additionally, the performance of the designed controller is also compared with actuator saturated H-infinity controller and the robustness of controller is tested for changing stiffness parameters. Simulation results indicate that superior earthquake induced vibration suppression is achieved by the use of designed controllers and active vibration control system.