In this paper, we have introduced an efficient Legendre wavelet spectral method (LWSM) to ship roll motion model for investigating the nonlinear damping coefficients. The accuracy of the proposed method is assessed by rolling with an initial amplitude using nonlinear type of equations. To the best of our knowledge until now there is no rigorous wavelet solution has been reported for the above model. Convergence analysis of the proposed method is discussed. The operational matrix of derivative is utilized to convert a ship roll motion equation into a set of algebraic equations. Accurate coefficients can be easily obtained for large rolling angles up to the amplitude at the maximum value of the restoring moment using wavelets. Some numerical examples are given to show the validity and applicability of the proposed wavelet method. Moreover the use of Legendre wavelets is found to be simple,flexible, accurate, efficient and small computation cost.