In this article, a collocation algorithm based on quintic B-splines is proposed to nd a numerical solution to the nonlinear Generalized Regularized Long Wave (GRLW) equation. Moreover, to analyze the linear stability of the numerical scheme, the von-Neumann technique is used. The numerical approach to three test examples consisting of a single solitary wave, the collision of two solitary waves, and the growth of an undular bore is discussed. The accuracy of the method is demonstrated by calculating the error in L2 and L 1 norms and the conservative quantities I 1 , I 2 and I 3 . The ndings are compared with those previously reported in the literature. Finally, the motion of solitary waves is graphically plotted according to di erent parameters.