This paper is concerned with networked output feedback H∞ control of an offshore structure under earthquakes. With a networked model of the offshore structure, a networked output feedback H∞ control strategy is proposed to suppress seismic vibration of the structure. Then, some delay-dependent stability criteria for the offshore structure system are derived. Simulation results show that compared with traditional network-free controllers, the networked output feedback H∞ controller can mitigate vibration of the offshore structure and control cost to a smaller level.