We conducted a numerical simulation that takes into account the effect of wave frequency dispersion in the Indian Ocean Tsunami that occurred on December 26, 2004. A leapfrog-implicit numerical scheme based on Shigihara et al. [6] is applicable to practical simulation. Dispersion effect is negligible for the runup to the northwest coast of Sumatra Island. At the west side of tsunami source, if the aim of simulation is the reproduction of detailed propagation process, dispersion should be considered in Sri Lanka. If maximum runup height and tsunami arrival time are required, however, dispersion may be negligible.