In this work, we construct the lumped Galerkin approach based on cubic B-splines to obtain the numerical solution of the generalized regularized long wave equation. Applying the von Neumann approximation, it is shown that the linearized algorithm is unconditionally stable. The presented method is implemented to three test problems including single solitary wave, interaction of two solitary waves and development of an undular bore. To prove the performance of the numerical scheme, the error norms L-2 and L-infinity and the conservative quantities I-1, I-2 and I-3 are computed and the computational data are compared with the earlier works. In addition, the motion of solitary waves is described at different time levels.