Abstract: Boussinesq equations have been verified to be accurate and revealing predictors of a wide range of nearshore hydrodynamic behaviour, including wave dispersion, shoaling, nonlinear interaction and a range of additional topics. In order to reduce the boundary reflection, a sponge boundary layer is usually integrated in the model, which can absorb wave energy in a rather wide frequency range. The paper presents a non-reflecting boundary condition using numerical dissipation approach in Boussinesq equations discrete. The calculation results of regular waves and random waves show that this method can provide the same simulations with the method of sponge layer. Since the method just uses a layer with the grid space increased gradually to dissipate the wave energy at the open boundary, and does not require modifying the model code, it is practical.