This paper is concerned with the active vibration control of multi-degreeof-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 output-feedback H-infinity controller is designed in this study. The time history of ground motion of the Northridge earthquake, 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 disturbance using ground motion of the Northridge Earthquake.