The linear shallow-water equations have been used frequently to simulate transoceanic propagation of tsunamis instead of the linear Boussinesq equations. In previous studies, the physical dispersion is compensated by using the numerical dispersion generated from the leap-frog finite difference scheme. However, the linear Boussinesq equations can be directly solved because computer technique has been improved dramatically. In this study, a new finite difference scheme is proposed to discretize the linear Boussinesq equations. The newly developed model is applied to propagation of a Gaussian hump over a constant water depth. The model is then verified by comparing predicted results with analytic solutions. Predicted results agree well with analytical solutions. The model can be directly applied to simulation of transoceanic propagation of tsunamis.