A new numerical simulation model with Boussinesq-typed equations for tsunamis is developed to reproduce a dispersive wave observed in the 1983 Nihonkai-Chubu earthquake tsunami. The present model has advantages with the multi regions simulation with nested grid system including runup. The two-step mixed finite difference method is selected as the numerical method because of numerical stability and high-speed calculation. Since the numerical simulation with dispersion effect and without breaking overestimates the value of the run-up, wave breaking model was developed in the model through the comparison with hydraulic experiment. We applied the model to the 1983 Nihonkai-Chubu earthquake tsunami. The tsunami heights on shoreline and inundation regions on land are obtained with numerical stability and we have results more higher and widely than those by the shallow water model.