Abstract: An approximate analytical solution with a certain precision helps to construct a link between ship rolling motion features and hull parameters，which is convenient for analyzing the influence of hull parameters on the rol-ling motion and stability． In this paper，by taking into consideration the nonlinearity of damping and restoring mo-ments，an equation describing the ship rolling motion in regular waves is established． Then，in order to overcome the limitations of weak nonlinearity，the modified Lindstedt-Poincare method (MLP) is adopted to obtain the per-turbation solution of the established rolling motion equation，and the analytical solution in still water which is accu-rate to the second order and the analytical solution in regular wave which is accurate to the first order are both ob-tained． Finally，the correctness of the approximate analytical solution is verified by an example solved respectively via the MLP method and the numerical algorithm．

Key words: ship rolling, nonlinearity, MLP method, approximate analysis