The aim of this study is to design a controller based on Lyapunov's direct method for fin roll stabilization systems for ships in beam seas. A third order mathematical model consisting of uncoupled roll motion of a ship and fin hydraulic system dynamics is considered. In the model, random wind force is defined by Gaussian white noise. Both controlled and uncontrolled roll motions are presented considering stall effect by roll-time history and safe basin graphics. It is observed from the results that fin control system is successful to reduce erosion percentages of safe basins and roll amplitudes.