In this research the stochastic nonlinear dynamic behaviors and probability density function of ship rolling are studied by nonlinear dynamic method and probability theory. The probability density function of rolling response is evaluated through solving the stochastic differential equations by using path integral method based on Gauss-Legendre interpolation scheme. The time-dependent probability of ship rolling restricted within the safe domain is provided and capsizing is investigated in the probability‟s view. The random differential equation of ships‟ rolling motion is established considering the nonlinear damping, nonlinear restoring moment, the white noise wave excitation, and the colored noise wave excitation. As an example, an ocean survey vessel T-AGOS is considered to sail in the seas of Pierson-Moskowitz wave spectrum. It is found that the probability decreases as time progresses and it decreases much more quickly for the high intensity of the noise. The ship will finally leave the safe domain and capsize in the probability‟s view. It is also shown the similarity of probability density contours between the case of white noise wave excitation and the case of colored noise wave excitation.