The previous real-time tsunami prediction based on the inversion method and the linear superposition can predict the tsunami in near shore area quickly, but it can not predict the tsunami inundation. The present study developed the empirical formula to estimate the overflow rate from the tsunami profile predicted by the previous method. Moreover, the level fill method was applied to predict the tsunami inundation from the estimated overflow rate. Numerical experiments using the actual topography and the historical earthquakes proved that the combination of the previous method, the empirical formula to estimate the overflow rate, and the level fill method can predict the tsunami inundation quickly from the offshore tsunami observation.