In this paper, the Adomian decomposition method is implemented to find the solution of the nonlinear generalized regularized long wave (GRLW) equation with appropriate initial conditions. The methodology of the method is investigated. The accuracy of the algorithm is illustrated by solving three test examples of the problem. We study the convergence analysis of the method. The results that will be obtained are compared with the analytical solutions, where we observe that only some terms of the series expansion are required to obtain approximation solutions with good accuracy. And also, this studying is extending to discuss the interaction of two and three solitons.