Based on a fourth-order Boussinesq model by Madsen and Sch?ffer, a numerical implementation of the model in one horizontal direction is established by finite difference method in staggered grids. A composite forth order Adams-Bashforth-Moulton scheme is used to step the model forward in time. A grid-interior source function presented by Gobbi and Kirby is utilized in present model to avoid the re-refraction. Numerical simulations of wave propagating over a submerged sill are carried out. And the Luth et al’s(1994) laboratory data are used to test the applicability of the present model, and the numerical results are in general agreement with laboratory data. In addition, numerical results based on the Boussinesq model in non-staggered grids are given. Results show that both models can well simulate the wave evolution over a submerged sill.