Abstract: In this paper, the numerical solution of a class of nonlinear Rosenau-KdV-RLW equations is studied by using the finite difference method. In order to improve the theoretical accuracy of the difference scheme, a new high-precision three-level extrapolation linearized difference scheme was constructed by performing extrapolation discretization in the temporal and spatial levels respectively.Numerical experiments have been conducted and the results show that the scheme is effective, and the theoretical accuracy of the spatial level can reach fourth order.