A new two-dimensional finite difference numerical scheme is developed to simulate the propagation of distant tsunamis over slowly varying topography with improved dispersion effect of waves. The new scheme solves the shallow water equations on a uniform grid system. However, the actual computation is made on a hidden grid system whose grid size is adjustable according to the condition required to satisfy local dispersion relationships of waves for varying water depth. The present model is tested for the cases of two-dimensional propagation of an initial Gaussian hump over various uniform water depth regions. For a varying topography, a one-dimensional test is conducted. The tests show that accuracy of the numerical model is improved significantly over that of the conventional finite difference models. Finally, the present model is applied to the simulation of a historical tsunami event. The numerical result shows that the submerged rise and ridge play an important role of a waveguide for the tsunamis propagating over that topography.