This paper is concerned with the active vibration control of a four-degree-of-freedom structure, which is effected by earthquake. To obtain desired time history and frequency responses for solution of active vibration control problem, Linear Matrix Inequality (LMI) based state-feedback mixed H-2/H-infinity controller is designed in this study. The time history of ground motion of the Kobe earthquake in 1995, which is a disturbance input, is applied to modeled structure. At the end of the study, the time history of the storey displacements, velocities and frequency responses of both controlled and uncontrolled cases are presented and results are discussed. Performance of the designed controller has been shown for the different loads and disturbances using ground motion of the Kocaeli earthquake.