The paper is concerned with a H(infinity) control of the slow drift oscillation of a moored floating platform (catenary shaped mooring chains were used). Slow drift oscillation appears as a result of resonance between the mooring system and the drifting force and the amplitude is very large, but it can be counteracted by thrusters because of its small exciting force. Our aim is to suppress slow drift oscillation using thruster activities that are not affected by wave frequency motion. The H(infinity) controller was designed using a simplified linear mathematical model obtained from nonlinear motion equations of a floating platform and mooring chains. Model tests were carried out and some successful experimental results were obtained. Moreover the simulated results were in good agreement with experimental ones.