An explicit one-dimensional model based on the shallow water equations (SWEs) was established in this work to simulate tsunami wave propagation on a vegetated beach. This model adopted the finite-volume method (FVM) for maintaining the mass balance of these equations. The resistance force caused by vegetation was taken into account as a source term in the momentum equation. The Harten–Lax–van Leer (HLL) approximate Riemann solver was applied to evaluate the interface fluxes for tracing the wet/dry transition boundary. This proposed model was used to simulate solitary wave run-up and long-periodic wave propagation on a sloping beach. The calibration process suitably compared the calculated results with the measured data. The tsunami waves were also simulated to discuss the water depth, tsunami force, as well as the current speed in absence of and in presence of forest domain. The results indicated that forest growth at the beach reduced wave energy loss caused by tsunamis. A series of sensitivity analyses were conducted with respect to variable parameters (such as vegetation densities, wave heights, wave periods, bed resistance, and beach slopes) to identify important influences on mitigating tsunami damage on coastal forest beach.