In this paper, a stochastic averaging method based on elliptic function is proposed to evaluate the probabilistic solution of ship roll motion excited by bounded noises. We carry out local sensitivity analysis on the rolling model to analyze the influence of main parameters, thus laying a foundation for the random analysis. By introducing the Jacobi elliptic functions (JEFs), we acquire the stochastic differential equation and the Ito equation regarding the amplitude and phase of the roll motion. Then, we obtain the probabilistic solutions of the rolling system by solving the corresponding Fokker-Planck-Kolmogorov (FPK) equation. Then apply this method to investigate the probabilistic solution of ship’s nonlinear rolling motion under bounded noise excitation, which shows perfect agreement with the sensitivity quantification. Finally, the feasibility and accuracy of the proposed technique are verified by the Monte Carlo simulations.