The evaluation on ship roll motion in seas has attracted many researchers in the field of science and engineering in the case of either deterministic or random excitation because overlarge motion will be a potential and life on the ship. For the case of random excitation. most efforts have been devoted to the moments of responses under continuous Gaussian white noise excitation. The probability density function (PDF) has been less addressed and other types of excitation are scarcely investigated (i.e. diserete Poisson of response white noise. In this paper. the stationary PDF solution to nonlinear ship roll motion subjected to Poisson white noise is analyzed. Under such random excitation, the stochastic roll response of ship can be evaluated by a joint continuous Markov model. According to this model, the joint PDF solution for the roll displacement and velocity is governed by the generalized Fokker-Planck-Kolmogorov (FPK) equation. Subsequently, the exponential polynomial closure EPC) method is adopted to solve the generalized FPK equation. In the EPC method, the PDF solution is assumed to be an exponential function of polynomials in state variables. Special measure is taken such that the generalized FPK equation is satisfied in average sense of integration with the assumed PDF·The problem of determining unknown parameters of the approximate PDF finally results in solving simultancous nonlinear algebraic equations In order to evaluate the effectiveness of the EPC method. numerical analysis is conducted. The results show that the result obtained with the EPC method (n-2) is the same as the results given by the equivalent linearization (EQL) method and the EQL. resuit differs a lot from the simulation result, especially in the tail region. When the polynomial (n) increases to 4 or 6. the EPC method presents a good result compared with the simulation even in the tail of the PDF