Parametric ship roll resonance is a phenomenon where a ship can rapidly develop high roll motion while sailing in longitudinal waves. This effect can be described mathematically by periodic changes of the parameters of the equations of motion, which lead to a bifurcation. In this paper, the control design of an active u-tank stabilizer is carried out using Lyapunov theory. A nonlinear backstepping controller is developed to provide global exponential stability of roll. An extension of commonly used u-tank models is presented to account for large roll angles, and the control design is tested via simulation on a high-fidelity model of a vessel under parametric roll resonance.