Modeling and forecasting of the sway of a moored vessel subjected to random waves were studied recently using quadratic digital filtering techniques. Moreover, it was observed that the future response of the vessel can be predicted with relatively high accuracy. This paper describes a control scheme, which utilizes a quadratic digital filter, to stabilize the low-frequency drift oscillation (LFDO) of moored vessels by a process , whose transfer function may be unknown or time-varying, and an appropriately chosen feedforward compensator. The feedforward compensator generates a control signal that counteracts the LFDO. The predictive filter coefficients are determined from experimental time series data of random sea excitation and the associated sway response of a scaled (1:48) moored barge. The parameters of the process are estimated using a recursive least squares (RLS) method. Simulation results show that the sway of the controlled vessel is reduced considerably, compared with that of a uncontrolled vessel.