A predictive controller can solve a control problem related to a disturbance-dominant system such as roll stabilization of a ship in waves. In this paper, a predictive controller is developed for a fin stabilizer. Future wave-induced moment is modeled simply using two typical regular wave components for which six parameters are identified by the recursive Fourier transform and the least squares method using the past time series of the roll motion. After predicting the future wave-induced moment, optimal control theory is applied to discover the most effective command fin angle that will stabilize the roll motion. In the results, wave prediction performance is investigated, and the effectiveness of the predictive controller is compared to a conventional PD controller.