This paper deals with the active vibration control of cranes against earthquake induced vibration. For this purpose, firstly a dynamic model is developed and then Linear Matrix Inequalities (LMIs) based mixed H-2/H-infinity state-feedback controller is designed in this study. 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 in 1999 (M-w=7,4), which is a disturbance input, is applied to modeled container crane. Additionally, the performance of the designed controller is also compared with a state-feedback H-infinity controller. Simulation results indicate that superior earthquake induced vibration suppression is achieved by the use of designed controllers and active vibration control system.