It is well known that truncated error of long wave simulation by the finite difference method appears as the dispersion or dissipation effects and causes numerical damping of wave height. In the present study, the truncated error of tsunami numerical simulation is investigated by using exact and approximate solutions of descretizated equations. As a result of one-dimensional initial value problem, it is clarified that numerical error varies dependently of Fourier spectrum of initial wave profile and resolution Δx/L and the value K(=√gh·Δt/Δx) are important parameters to estimate truncated error.