Based on the extended Boussinesq equation with weak nonlinearity, 2-D numerical model was established in nonstaggered grids by the finite difference method. The nonstaggered grids were used with the first-order spatial derivatives being discretized by the fourth-order and the second-order terms discertized by the second-order. For the time derivatives, a composite fourth-order accurate Adams-Bashforth Moulton scheme was used. Numerical simulation was done upon one-dimension and two-dimension wave propagations problem, and through the comparisons of numerical results with the related experimental data, the application of the extended Boussinesq equations were investigated.